Maharashtra Board Practice Set 30 Class 6 Maths Solutions Chapter 12 Percentage

Balbharti Maharashtra State Board Class 6 Maths Solutions covers the Std 6 Maths Chapter 12 Percentage Class 6 Practice Set 30 Answers Solutions.

6th Standard Maths Practice Set 30 Answers Chapter 12 Percentage

Question 1.
Shabana scored 736 marks out of 800 in her exams. What was the percentage she scored?
Solution:
Total marks of the examination = 800
Marks scored by Shabana = 736
Suppose Shabana scored A% marks.
Maharashtra Board Class 6 Maths Solutions Chapter 12 Percentage Practice Set 30 1
∴ A = 92%
∴ Shabana scored 92% marks.

Question 2.
There are 500 students in the school in Dahihanda village. If 350 of them can swim, what percent of them can swim and what percent cannot?
Solution:
Total number of students in the school = 500
Number of students who can swim = 350
Suppose A% students can swim.
Maharashtra Board Class 6 Maths Solutions Chapter 12 Percentage Practice Set 30 2
∴ A = 70%
Percentage of students who cannot swim = 100% – Percentage of students who can swim .
= 100% – 70% = 30%
∴ 70% of the students can swim and 30% cannot swim.

Question 3.
If Prakash sowed jowar on 75% of the 19500 sq. m. of his land, on how many sq. m. did he actually plant jowar?
Solution:
Total area of the land = 19500 sq. m.
Percentage of area in which Prakash sowed jowar = 75%
Suppose Prakash planted jowar in A sq. m.
Maharashtra Board Class 6 Maths Solutions Chapter 12 Percentage Practice Set 30 3
∴ A = 14,625 sq. m.
∴ Prakash planted jowar in 14,625 sq.m.

Question 4.
Soham received 40 messages on his birthday. Of these, 90% were birthday greetings. How many other messages did he get besides the greetings?
Solution:
Total messages received by Soham on his birthday = 40
Percentage of messages received for birthday greetings = 90%
Suppose Soham got A number of birthday greetings.
Maharashtra Board Class 6 Maths Solutions Chapter 12 Percentage Practice Set 30 4
∴ A = 36
∴ Number of messages received other than birthday greetings
= total messages received – total number of birthday greetings
= 40 – 36 = 4
∴ The number of messages received other than birthday greetings is 4.

Question 5.
Of the 5675 people in a village 5448 are literate. What is the percentage of literacy in the village?
Solution:
Number of people in the village = 5675
Number of people who are literate = 5448
Suppose the percentage of literacy in the village is A%.
Maharashtra Board Class 6 Maths Solutions Chapter 12 Percentage Practice Set 30 5
∴ A = 96%
∴ The percentage of literacy in the village is 96%.

Question 6.
In the elections, 1080 of the 1200 women in Jambhulgaon cast their vote, while 1360 of the 1700 in Wadgaon cast theirs. In which village did a greater proportion of women cast their votes?
Solution:
Total number of women in Jambhulgaon = 1200
Number of women in Jambhulgaon who voted = 1080
Suppose A% women cast their vote in Jambhulgaon village.
Maharashtra Board Class 6 Maths Solutions Chapter 12 Percentage Practice Set 30 6
Maharashtra Board Class 6 Maths Solutions Chapter 12 Percentage Practice Set 30 7
∴ A = 90%
In Jambhulgaon, the percentage of women who voted in the elections was 90%.
Total number of women in Wadgaon = 1700 Number of women in Wadgaon who voted = 1360
Suppose B% women cast their vote in Wadgaon.
Maharashtra Board Class 6 Maths Solutions Chapter 12 Percentage Practice Set 30 8
∴ B = 80%
∴ In Wadgaon, the percentage of women who voted in the elections was 80%.
∴ A greater proportion of women cast their votes in Jambhulgaon.

Maharashtra Board Class 6 Maths Chapter 12 Percentage Practice Set 30 Intext Questions and Activities

Question 1.
There are 9 squares in the figure alongside. The letters ABCDEFGHI are written in squares. Give each of the letters a unique number from 1 to 9 so that every letter has a different number.
Besides, A + B + C = C + D + E = E + F + G = G + H + I should also be true. (Textbook pg. no. 64)
Maharashtra Board Class 6 Maths Solutions Chapter 12 Percentage Practice Set 30 9
Solution:
Maharashtra Board Class 6 Maths Solutions Chapter 12 Percentage Practice Set 30 10
(This is one of the possible solutions of the above riddle. There are more solutions possible.)

Maharashtra Board Practice Set 5 Class 6 Maths Solutions Chapter 3 Integers

Balbharti Maharashtra State Board Class 6 Maths Solutions covers the Std 6 Maths Chapter 3 Integers Class 6 Practice Set 5 Answers Solutions.

6th Standard Maths Practice Set 5 Answers Chapter 3 Integers

Question 1.
Add:

  1. 8 + 6
  2. 9 + (-3)
  3. 5 + (-6)
  4. – 7 + 2
  5. – 8 + 0
  6. – 5 + (-2)

Solution:

1. 8 + 6 = (+8) + (+6) = +14 2. 9 + (-3) = (+9) + (- 3) = +6 3. 5 + (-6) = (+5) + (-6) = -1
4. -7 + 2 = (-7) + (+2) = -5 5. -8 + 0 = (-8) + 0 = -8 6. -5 + (-2) = (-5) + (-2) = -7

Question 2.
Complete the table given below:

+ 8 4 -3 -5
-2 -2 + 8 = +6
6
0
-4

Solution:

+ 8 4 -3 -5
-2 (-2) + (+8) = +6 (-2) +(+4) = 2 (-2) +(-3) =-5 (-2) +(-5) =-7
6 (+6) + (+8) = 14 (+6) + (+4) = 10 (+6) + (-3) = 3 (+6) + (-5) = 1
0 0 + (+8) = 8 0 + (+4) = 4 0 + (-3) = -3 0 + (-5) = -5
-4 (-4) + (+8) = 4 (-4) +(+4) = 0 (-4) + (-3) = -7 (-4) + (-5) = -9

Maharashtra Board Class 6 Maths Chapter 3 Integers Practice Set 5 Intext Questions and Activities

Question 1.
On the playground, mark a timeline showing the years from 2000 to 2024. With one child standing at the position of the 2017, ask the following questions: (Textbook pg. no. 15)

  1. While playing this game, what is his/her age?
  2. Five years ago, which year was it? And what was his / her age then?
  3. In which year will he / she go to Std X? How old will he / she be then?

The child should find answers to such questions by walking the right number of units and in the right direction on the timeline.
[Assume child born year is 2009]
Solutions:

  1. Age of child is 8 years.
  2. Five years ago, year was 2012. His/her age is 3 years.
  3. In 2024, he/she will go the Std X. His/her age is 15 years.

Question 2.
On a playground mark a timeline of 100 years. This will make it possible to count the years from 0 to 2100 on it. Important historical events can then be shown in proper centuries. (Textbook pg. no. 16)
Solution:
(Students should attempt this activity on their own)

Question 3.
Observe the figures and write appropriate number in the boxes given below. (Textbook pg. no. 16 and 17)
i.

Maharashtra Board Class 6 Maths Solutions Chapter 3 Integers Practice Set 5 1
a. At first the rabbit was at the number ____
b. It hopped ___ units to the right.
c. It is now at the number ___
Solution:
i.
a. +1
b. 5
c. +6

ii.
Maharashtra Board Class 6 Maths Solutions Chapter 3 Integers Practice Set 5 2
a. At first the rabbit was at the number ___
b. It hopped ____ units to the right.
c. It is now at the number ____
Solution:
ii.
a. -2
b. 5
c. +3

iii.
Maharashtra Board Class 6 Maths Solutions Chapter 3 Integers Practice Set 5 3
a. At first the rabbit was at the number ___
b. It hopped ____ units to the left.
c. It is now at the number ___
Solution:
iii.
a. -3
b. 4
c. -7

iv.
Maharashtra Board Class 6 Maths Solutions Chapter 3 Integers Practice Set 5 4
a. At first the rabbit was at the number ___
b. It hopped___units to the left.
c. It is now at the number ____
Solution:
iv.
a. +3
b. 4
c. -1

Maharashtra Board Practice Set 40 Class 6 Maths Solutions Chapter 17 Geometrical Constructions

Balbharti Maharashtra State Board Class 6 Maths Solutions covers the Std 6 Maths Chapter 17 Geometrical Constructions Class 6 Practice Set 40 Answers Solutions.

6th Standard Maths Practice Set 40 Answers Chapter 17 Geometrical Constructions

Question 1.
Draw line l. Take point P anywhere outside the line. Using a set square draw a line PQ perpendicular to line l.
Solution:
Step 1:
Maharashtra Board Class 6 Maths Solutions Chapter 17 Geometrical Constructions Practice Set 40 1

Step 2:
Maharashtra Board Class 6 Maths Solutions Chapter 17 Geometrical Constructions Practice Set 40 2
line PQ ⊥ line l.

Question 2.
Draw line AB. Take point M anywhere outside the line. Using a compass and ruler, draw a line MN perpendicular to line AB.
Solution:
Step 1:
Maharashtra Board Class 6 Maths Solutions Chapter 17 Geometrical Constructions Practice Set 40 3

Step 2:
Maharashtra Board Class 6 Maths Solutions Chapter 17 Geometrical Constructions Practice Set 40 4

Step 3:
Maharashtra Board Class 6 Maths Solutions Chapter 17 Geometrical Constructions Practice Set 40 5
line MN ⊥ line AB.

Question 3.
Draw a line segment AB of length 5.5 cm. Bisect it using a compass and ruler.
Solution:
Step 1:
Maharashtra Board Class 6 Maths Solutions Chapter 17 Geometrical Constructions Practice Set 40 6

Step 2:
Maharashtra Board Class 6 Maths Solutions Chapter 17 Geometrical Constructions Practice Set 40 7
line MN is the perpendicular bisector of seg AB.

Question 4.
Take point R on line XY. Draw a perpendicular to XY at R, using a set square.
Solution:
Step 1:
Maharashtra Board Class 6 Maths Solutions Chapter 17 Geometrical Constructions Practice Set 40 8

Step 2:
Maharashtra Board Class 6 Maths Solutions Chapter 17 Geometrical Constructions Practice Set 40 9
line TR ⊥ line XY.

Maharashtra Board Class 6 Maths Chapter 17 Geometrical Constructions Practice Set 40 Questions and Activities

Question 1.
In the above construction, why must the distance in the compass be kept constant? (Textbook pg. no. 90)
Solution:
The point N is at equal distance from points P and Q.
If we change the distance of the compass while drawing arcs from points P and Q, we will not get a point which is at equal distance from P and Q. Hence, the distance in the compass must be kept constant.

Question 2.
The Perpendicular Bisector. (Textbook pg. no. 90)
Maharashtra Board Class 6 Maths Solutions Chapter 17 Geometrical Constructions Practice Set 40 10

  1. A wooden ‘yoke’ is used for pulling a bullock cart. How is the position of the yoke determined?
  2. To do that, a rope is used to measure equal distances from the spine/midline of the bullock cart. Which geometrical property is used here?
  3. Find out from the craftsmen or from other experienced persons, why this is done.

Solution:

  1. For the bullock cart to be pulled in the correct direction by the yoke, its Centre O should be equidistant from the either sides of the cart.
  2. The property of perpendicular bisector is used to make the point equidistant from both the ends
  3. A rope is used just like a compass to get equal distances from the spine/midline of bullock cart.

Question 3.
Take a rectangular sheet of paper. Fold the paper so that the lower edge of the paper falls on its top edge, and fold it over again from right to left. Observe the two folds that have formed on the . paper. Verify that each fold is a perpendicular bisector of the other. Then measure the following distances. (Textbook pg. no. 91)
i. l(XP)
ii. l(XA)
iii. l(XB)
iv. l(YP)
v. l(YA)
Maharashtra Board Class 6 Maths Solutions Chapter 17 Geometrical Constructions Practice Set 40 11
You will observe that l(XP) = l(YP), l(XA) = l(YA) and l(XB) = l(YB)
Therefore we can conclude that all points on the vertical fold (perpendicular bisector) are equidistant from the endpoints of the horizontal fold.
Solution:
[Note: Students should attempt this activity on their own.]

Maharashtra Board Practice Set 19 Class 6 Maths Solutions Chapter 6 Bar Graphs

Balbharti Maharashtra State Board Class 6 Maths Solutions covers the Std 6 Maths Chapter 6 Bar Graphs Class 6 Practice Set 19 Answers Solutions.

6th Standard Maths Practice Set 19 Answers Chapter 6 Bar Graphs

Question 1.
The names of the heads of some families in a village and the quantity of drinking water their family consumes in one day are given below. Draw a bar graph for this data.
(Scale: On Y axis. 1 cm = 10 liters of water)

Name Ramesh Shobha Ayub Julie Rahul
Liters of water Used 30 L 60 L 40 L 50L 55 L

Solution:
Maharashtra Board Class 6 Maths Solutions Chapter 6 Bar Graphs Practice Set 19 1

Question 2.
The names and numbers of animals in a certain zoo are given below. Use the data to make a bar graph. (Scale: On Y axis, 1 cm = 4 animals).

Animals Deer Tiger Monkey Rabbit Peacock
Number 20 4 12 16 8

Solution:
Maharashtra Board Class 6 Maths Solutions Chapter 6 Bar Graphs Practice Set 19 2

Question 3.
The table below gives the number of children who took part in the various items of the talent show as part of the annual school gathering. Make a bar graph to show this data.
(Scale: On Y-axis, 1 cm = 4 children)

Programme Theater Dance Vocal music Instrumental music One-act plays
Number of Children 24 40 16 8 4

Solution:
Maharashtra Board Class 6 Maths Solutions Chapter 6 Bar Graphs Practice Set 19 3

Question 4.
The number of customers who came to a juice centre during one week is given in the table below. Make two different bar graphs to show this data.
(On Y-axis, 1 cm = 10 customers, 1 cm = 5 customers)

Type of juice Orange Pineapple Apple Mango Pomegranate
Number of customers 50 30 25 65 10

Solution:
Maharashtra Board Class 6 Maths Solutions Chapter 6 Bar Graphs Practice Set 19 4
Maharashtra Board Class 6 Maths Solutions Chapter 6 Bar Graphs Practice Set 19 5

Question 5.
Students planted trees in 5 villages of Sangli district. Make a bar graph of this data. (Scale: On Y-axis, 1 cm = 100 trees).

Name of Place Dudhgaon Bagni Samdoli Ashta Kavathepiran
Number of Trees Planted 500 350 600 420 540

Solution:
Maharashtra Board Class 6 Maths Solutions Chapter 6 Bar Graphs Practice Set 19 6

Question 6.
Yashwant gives different amounts of time as shown below, to different exercises he does during the week. Draw a bar graph to show the details of his schedule using an appropriate scale.

Type of exercise Running Yogasanas Cycling Mountaineering Badminton
Time 35 minutes 50 minutes 1 hr 10 min \(1\frac { 1 }{ 2 }\) hours 45 minutes

Solution:
1 hour = 60 minutes
∴ 1 hour 10 minutes = 1 hour + 10 minutes = 60 minutes +10 minutes = 70 minutes
and \(1\frac { 1 }{ 2 }\) hours = 1 hour + \(\frac { 1 }{ 2 }\) hour = 60 minutes + 30 minutes = 90 minutes
The given table can be written as follows:

Type of Exercise Running Yogasanas Cycling Moutaineering Badminton
Time 35 minutes 50 minutes 70 minutes 90 minutes 45 minutes

Maharashtra Board Class 6 Maths Solutions Chapter 6 Bar Graphs Practice Set 19 7

Question 7.
Write the names of four of your classmates. Beside each name, write his/her weight in kilograms. Enter this data in a table like the above and make a bar graph.
Solution:

Name of classmates Weight (kg)
Rohan 32
Laxmi 28
Rakesh 40
Riya 36

Scale: On Y-axis, 1 cm = 4 kg [Note: Students can take their own examples]
Maharashtra Board Class 6 Maths Solutions Chapter 6 Bar Graphs Practice Set 19 8

Maharashtra Board Class 6 Maths Chapter 6 Bar Graphs Practice Set 19 Intext Questions and Activities

Question 1.
Collect bar graphs from newspapers or periodicals showing a variety of data. (Textbook pg. no. 38)
Solution:
(Student should attempt the activities on their own.)

Maharashtra Board Practice Set 7 Class 6 Maths Solutions Chapter 3 Integers

Balbharti Maharashtra State Board Class 6 Maths Solutions covers the Std 6 Maths Chapter 3 Integers Class 6 Practice Set 7 Answers Solutions.

6th Standard Maths Practice Set 7 Answers Chapter 3 Integers

Question 1.
Write the proper signs >, < or = in the boxes below:

  1. -4 __ 5
  2. 8 __ -10
  3. +9 __ +9
  4. -6 __ 0
  5. 7 __ 4
  6. 3 __ 0
  7. -7 __ 7
  8. -12 __ 5
  9. -2 __ -8
  10. -1 __ -2
  11. 6 __ -3
  12. -14 __ -14

Solution:

  1. -4 < 5
  2. 8 > -10
  3. +9 = +9
  4. -6 < 0
  5. 7 > 4
  6. 3 > 0
  7. -7 < 7
  8. -12 < 5
  9. -2 > -8
  10. -1 > -2
  11. 6 > -3
  12. -14 = -14

Maharashtra Board Practice Set 6 Class 6 Maths Solutions Chapter 3 Integers

Balbharti Maharashtra State Board Class 6 Maths Solutions covers the Std 6 Maths Chapter 3 Integers Class 6 Practice Set 6 Answers Solutions.

6th Standard Maths Practice Set 6 Answers Chapter 3 Integers

Question 1.
Write the opposite number of each of the numbers given below.

Number 47 +52 -33 -84 -21 +16 -26 80
Opposite number

Solution:

Number 47 +52 -33 -84 -21 +16 -26 80
Opposite number -47 -52 +33 +84 +21 -16 +26 -80

Maharashtra Board Practice Set 28 Class 6 Maths Solutions Chapter 11 Ratio-Proportion

Balbharti Maharashtra State Board Class 6 Maths Solutions covers the Std 6 Maths Chapter 11 Ratio-Proportion Class 6 Practice Set 28 Answers Solutions.

6th Standard Maths Practice Set 28 Answers Chapter 11 Ratio-Proportion

6th Standard Maths Practice Set 28 Question 1.
In each example below, find the ratio of the first number to the second:
i. 24, 56
ii. 63,49
iii. 52, 65
iv. 84, 60
v. 35, 65
vi. 121, 99
Solution:
i. 24, 56
\(\frac{24}{56}=\frac{24 \div 8}{56 \div 8}=\frac{3}{7}\)
= 3:7

ii. 63,49
\(\frac{63}{49}=\frac{63 \div 7}{49 \div 7}=\frac{9}{7}\)
= 9:7

iii. 52, 65
\(\frac{52}{65}=\frac{52 \div 13}{65 \div 13}=\frac{4}{5}\)
= 4:5

iv. 84, 60
\(\frac{84}{60}=\frac{84 \div 12}{60 \div 12}=\frac{7}{5}\)
= 7:5

v. 35, 65
\(\frac{35}{65}=\frac{35 \div 5}{65 \div 5}=\frac{7}{13}\)
= 7:13

vi. 121, 99
\(\frac{121}{99}=\frac{121 \div 11}{99 \div 11}=\frac{11}{9}\)
= 11:9

6th Maths Practice Set 28 Question 2.
Find the ratio of the first quantity to the second.
i. 25 beads, 40 beads
ii. Rs 40, Rs 120
iii. 15 minutes, 1 hour
iv. 30 litres, 24 litres
v. 99 kg, 44000 grams
vi. 1 litre, 250 ml
vii. 60 paise, 1 rupee
viii. 750 grams, \(\frac { 1 }{ 2 }\) kg
ix. 125 cm, 1 metre
Solution:
i. Required Ratio = \(\frac{25}{40}=\frac{25 \div 5}{40 \div 5}=\frac{5}{8}\)

ii. Required Ratio = \(\frac{40}{120}=\frac{40 \div 40}{120 \div 40}=\frac{1}{3}\)

iii. 1 hour = 60 minutes
Required Ratio = \(\frac{15}{60}=\frac{15 \div 15}{60 \div 15}=\frac{1}{4}\)

iv. Required Ratio = \(\frac{30}{24}=\frac{30 \div 6}{24 \div 6}=\frac{5}{4}\)

v. 99 kg = 99 x 1000 grams = 99000 grams
Required Ratio = \(\frac{99000}{44000}=\frac{99000 \div 1000}{44000 \div 1000}=\frac{99}{44}\)
= \(\frac{99}{44}=\frac{99 \div 11}{44 \div 11}=\frac{9}{4}\)

vi. 1 litre, 250 ml
1 litre = 1000 ml
Required Ratio = \(\frac{1000}{250}=\frac{1000 \div 10}{250 \div 10}=\frac{100}{25}\)
= \(\frac{100}{25}=\frac{100 \div 25}{25 \div 25}=\frac{4}{1}\)

viii. 750 grams, \(\frac { 1 }{ 2 }\) kg
\(\frac { 1 }{ 2 }\) kg = \(\frac { 1000 }{ 2 }\) grams = 500 grams
Required Ratio = \(\frac{750}{500}=\frac{750 \div 10}{500 \div 10}=\frac{75}{50}\)
= \(\frac{75}{50}=\frac{75 \div 25}{50 \div 25}=\frac{3}{2}\)

ix. 125 cm, 1 metre
1 metre = 100 cm
Required Ratio = \(\frac{125}{100}=\frac{125 \div 25}{100 \div 25}=\frac{5}{4}\)

6th Std Maths Practice Set 28 Question 3.
Reema has 24 notebooks and 18 books. Find the ratio of notebooks to books.
Solution:
Ratio of notebooks to books
Maharashtra Board Class 6 Maths Solutions Chapter 11 Ratio-Proportion Practice Set 28 1
∴ The ratio of notebooks to books with Reema is \(\frac { 4 }{ 3 }\)

Practice Set 28 Question 4.
30 cricket players and 20 kho-kho players are training on a field. What is the ratio of cricket players to the total number of players?
Solution:
Total number of players = Cricket players + Kho-kho players
= 30 + 20 = 50
Ratio of cricket players to the total number of players
Maharashtra Board Class 6 Maths Solutions Chapter 11 Ratio-Proportion Practice Set 28 2
∴ The ratio of cricket players to the total number of players is \(\frac { 3 }{ 5 }\).

Question 5.
Snehal has a red ribbon that is 80 cm long and a blue ribbon 2.20 m long. What is the ratio of the length of the red ribbon to that of the blue ribbon?
Solution:
1 metre =100 cm
Length of the red ribbon = 80 cm
Length of the blue ribbon = 2.20 m = 2.20 x 100 cm
\(=\frac{220}{100} \times \frac{100}{1}=\frac{220 \times 100}{100 \times 1}\)
= 220 cm
∴ Ratio of length of the red ribbon to that of the blue ribbon
Maharashtra Board Class 6 Maths Solutions Chapter 11 Ratio-Proportion Practice Set 28 3
∴ The ratio of the length of the red ribbon to that of the blue ribbon is \(\frac { 4 }{ 11 }\).

11 Ratio Question 6.
Shubham’s age today is 12 years and his father’s is 42 years. Shubham’s mother is younger than his father by 6 years. Find the following ratios.
i. Ratio of Shubham’s age today to his mother’s age today.
ii. Ratio of Shubham’s mother’s age today to his father’s age today.
iii. The ratio of Shubham’s age to his mother’s age when Shubham was 10 years old.
Solution:
Shubham’s age today = 12 years
Shubham’s father’s age = 42 years
Shubham’s mother age = Shubham’s father’s age – 6 years
= 42 years – 6 years = 36 years

i. Ratio of Shubham’s age today to his mother’s age today
Maharashtra Board Class 6 Maths Solutions Chapter 11 Ratio-Proportion Practice Set 28 4
∴ The ratio of Shubham’s age today to his mother’s age today is \(\frac { 1 }{ 3 }\).

ii. Ratio of Shubham’s mother age today to his father’s age today
Maharashtra Board Class 6 Maths Solutions Chapter 11 Ratio-Proportion Practice Set 28 5
∴ The ratio of Shubham’s mother’s age today to his father’s age today is \(\frac { 6 }{ 7 }\).

iii. Shubham’s age today is 12 years and his mothers age is 36 years.
Hence when Shubham’s age was 10 years, his mother’s age was 34 years (i.e. 36 – 2 years).
Ratio of Shubham’s age to his mother’s age when Shubham was 10 years old
Maharashtra Board Class 6 Maths Solutions Chapter 11 Ratio-Proportion Practice Set 28 6
∴ The ratio of Shubham’s age to his mother’s age when Shubham was 10 years old is \(\frac { 5 }{ 17 }\)

Maharashtra Board Class 6 Maths Chapter 11 Ratio-Proportion Practice Set 28 Intext Questions and Activities

Question 1.
In the figure, colour some squares with any colour you like and leave some blank. (Textbook pg. no. 57)
Maharashtra Board Class 6 Maths Solutions Chapter 11 Ratio-Proportion Practice Set 28 7
i. Count all the boxes and write the number.
ii. Count the colored ones and write the number.
iii. Count the blank ones and write the number.
iv. Find the ratio of the colored boxes to the blank ones.
v. Find the ratio of the colored boxes to the total boxes.
vi. Find the ratio of the blank boxes to the total boxes.
Solution:
i. The number of all boxes is 16.
ii. The number of colored boxes is 7.
iii. The number of blank boxes is 9.
iv. Ratio of the colored boxes to the blank ones
Maharashtra Board Class 6 Maths Solutions Chapter 11 Ratio-Proportion Practice Set 28 8
v. Ratio of the colored boxes to the total boxes
Maharashtra Board Class 6 Maths Solutions Chapter 11 Ratio-Proportion Practice Set 28 9
vi. Ratio of the blank boxes to the total boxes
Maharashtra Board Class 6 Maths Solutions Chapter 11 Ratio-Proportion Practice Set 28 10

Maharashtra Board Practice Set 38 Class 6 Maths Solutions Chapter 16 Quadrilaterals

Balbharti Maharashtra State Board Class 6 Maths Solutions covers the Std 6 Maths Chapter 16 Quadrilaterals Class 6 Practice Set 38 Answers Solutions.

6th Standard Maths Practice Set 38 Answers Chapter 16 Quadrilaterals

Question 1.
Draw ₹XYZW and answer the following:
i. The pairs of opposite angles.
ii. The pairs of opposite sides.
iii. The pairs of adjacent sides.
iv. The pairs of adjacent angles.
v. The diagonals of the quadrilateral.
vi. The name of the quadrilateral in different ways.
Solution:
Maharashtra Board Class 6 Maths Solutions Chapter 16 Quadrilaterals Practice Set 38 1
i. a. ∠XYZ and ∠XWZ
b. ∠YXW and ∠YZW

ii. a. side XY and side WZ
b. side XW and side YZ

iii. a. side XY and side XW
b. side WX and side WZ
c. side ZW and side ZY
d. side YZ and side YX

iv. a. ∠XYZ and ∠YZW
b. ∠YZW and ∠ZWX
c. ∠ZWX and ∠WXY
d. ∠WXY and ∠XYZ

v. Seg XZ and seg YW

vi. ₹XYZW
₹YZWX
₹ZWXY
₹WXYZ
₹XWZY
₹WZYX
₹ZYXW
₹YXWZ

Question 2.
In the table below, write the number of sides the polygon has.

Names Quadrilateral Octagon Pentagon Heptagon Hexagon
Number of sides

Solution:

Names Quadrilateral Octagon Pentagon Heptagon Hexagon
Number of sides 4 8 5 7 6

Question 3.
Look for examples of polygons in your surroundings. Draw them.
Solution:
Maharashtra Board Class 6 Maths Solutions Chapter 16 Quadrilaterals Practice Set 38 2

Question 4.
We see polygons when we join the tips of the petals of various flowers. Draw these polygons and write down the number of sides of each polygon.
Solution:
Maharashtra Board Class 6 Maths Solutions Chapter 16 Quadrilaterals Practice Set 38 3
Maharashtra Board Class 6 Maths Solutions Chapter 16 Quadrilaterals Practice Set 38 4

Question 5.
Draw any polygon and divide it into triangular parts as shown here. Thus work out the sum of the measures of the angles of the polygon.
Maharashtra Board Class 6 Maths Solutions Chapter 16 Quadrilaterals Practice Set 38 5
Solution:
Maharashtra Board Class 6 Maths Solutions Chapter 16 Quadrilaterals Practice Set 38 6
Hexagon ABCDEF can be divided in 4 triangles namely ∆BAF, ∆BFE, ∆BED and ∆BCD
Sum of the measures of the angles of a triangle = 180°
∴ Sum of measures of the angles of the polygon ABCDEF = Sum of the measures of all the four triangles
= 180° + 180° + 180°+ 180°
= 720°
∴ The sum of the measures of the angles of the given polygon (hexagon) is 720°.

Maharashtra Board Class 6 Maths Chapter 16 Quadrilaterals Practice Set 38 Intext Questions and Activities

Question 1.
From your compass boxes, collect set squares of the same shapes and place them side by side in all possible different ways. What figures do you get? Write their names. (Textbook pg. no. 85)
a. Two set squares
b. Three set squares
c. four set squares
Solution:
a. Two set squares
Maharashtra Board Class 6 Maths Solutions Chapter 16 Quadrilaterals Practice Set 38 7

b. Three set squares
Maharashtra Board Class 6 Maths Solutions Chapter 16 Quadrilaterals Practice Set 38 8

c. four set squares
Maharashtra Board Class 6 Maths Solutions Chapter 16 Quadrilaterals Practice Set 38 9

Question 2.
Kaprekar Number. (Textbook pg. no. 86)
i. Take any 4-digit number in which all the digits are not the same.
ii. Obtain a new 4-digit number by arranging the digits in descending order.
iii. Obtain another 4-digit number by arranging the digits of the new number in ascending order.
iv. Subtract the smaller of these two new numbers from the bigger number. The difference obtained will be a 4-digit number. If it is a 3-digit number, put a 0 in the thousands place. Repeat the above steps with the difference obtained as a result of the subtraction.
v. After some repetitions, you will get the number 6174. If you continue to repeat the same steps you will get the number 6174 every time. Let us begin with the number 8531.
8531 → 7173 → 6354 → 3087 → 8352 → 6174 → 6174
This discovery was made by the mathematician, Dattatreya Ramchandra Kaprekar. That is why the number 6174 was named the Kaprekar number.
Solution:
Maharashtra Board Class 6 Maths Solutions Chapter 16 Quadrilaterals Practice Set 38 10

Maharashtra Board Practice Set 39 Class 6 Maths Solutions Chapter 17 Geometrical Constructions

Balbharti Maharashtra State Board Class 6 Maths Solutions covers the Std 6 Maths Chapter 17 Geometrical Constructions Class 6 Practice Set 39 Answers Solutions.

6th Standard Maths Practice Set 39 Answers Chapter 17 Geometrical Constructions

Question 1.
Draw line l. Take any point P on the line. Using a set square, draw a line perpendicular to line l at the point P.
Solution:
Step 1:
Maharashtra Board Class 6 Maths Solutions Chapter 17 Geometrical Constructions Practice Set 39 1

Step 2:
Maharashtra Board Class 6 Maths Solutions Chapter 17 Geometrical Constructions Practice Set 39 2
line PQ ⊥ line l

Question 2.
Draw a line AB. Using a compass, draw a line perpendicular to AB at point B.
Solution:
Step 1:
Maharashtra Board Class 6 Maths Solutions Chapter 17 Geometrical Constructions Practice Set 39 3

Step 2:
Maharashtra Board Class 6 Maths Solutions Chapter 17 Geometrical Constructions Practice Set 39 4

Step 3:
Maharashtra Board Class 6 Maths Solutions Chapter 17 Geometrical Constructions Practice Set 39 5
line BC ⊥ line AB.

Question 3.
Draw line CD. Take any point M on the line. Using a protractor, draw a line perpendicular to line CD at the point M.
Solution:
Step 1:
Maharashtra Board Class 6 Maths Solutions Chapter 17 Geometrical Constructions Practice Set 39 6

Step 2:
Maharashtra Board Class 6 Maths Solutions Chapter 17 Geometrical Constructions Practice Set 39 7
line MN ⊥ line CD

Maharashtra Board Class 6 Maths Chapter 17 Geometrical Constructions Practice Set 39 Questions and Activities

Question 1.
When constructing a building, what is the method used to make sure that a wall is exactly upright? What does the mason in the picture have in his hand? What do you think is his purpose for using it? (Textbook pg. no. 87)
Maharashtra Board Class 6 Maths Solutions Chapter 17 Geometrical Constructions Practice Set 39 8
Solution:
When constructing a building, a weight (usually with a pointed tip at the bottom) suspended from a string called as plummet or plump bob is aligned from the top of the wall to make sure that the wall is built exactly upright.
The mason in the picture is holding a plumb bob.
The string of the plumb bob is suspended from the top of the wall, such that plumb bob hangs freely. By observing whether the vertical wall is parallel to the string we can check if the constructed wall is vertical.

Question 2.
Have you looked at lamp posts on the roadside? How do they stand? (Textbook pg. no. 87)
Solution:
The lamp posts on the road side are standing erect or vertical.

Question 3.
For the above explained construction, why must we take a distance greater than half of the length of AB? What will happen if we take a smaller distance? (Textbook pg. no. 88)
Solution:
For the above construction, in step-3 we take distance greater than half of the length of AB, so that the arcs drawn by keeping the compass on points A and B intersect each other at point Q.
If the distance in compass is less than half of the length of AB, then the arcs drawn by keeping the compass at A and B will not intersect each other.

Maharashtra Board Practice Set 4 Class 6 Maths Solutions Chapter 3 Integers

Balbharti Maharashtra State Board Class 6 Maths Solutions covers the Std 6 Maths Chapter 3 Integers Class 6 Practice Set 4 Answers Solutions.

6th Standard Maths Practice Set 4 Answers Chapter 3 Integers

Question 1.
Classify the following numbers as positive numbers and negative numbers.
-5, +4, -2, 7, +26, -49, -37, 19, -25, +8, 5, -4, -12, 27
Solution:

Positive Numbers +4, 7, +26, 19, +8, 5, 27
Negative Numbers -5, -2, -49, -37, -25, -4, -12

Question 2.
Given below are the temperatures in some cities. Write them using the proper signs.

Place Shimla Leh Delhi Nagpur
Temperature 7 °C below 0° 12 °C below 0° 22 °C above 0° 31 °C above 0°

Solution:

Place Shimla Leh Delhi Nagpur
Temperature with proper sign -7 °C -12 °C +22 °C +31 °C

Question 3.
Write the numbers in the following examples using the proper signs.

  1. A submarine is at a depth of 512 meters below sea level.
  2. The height of Mt Everest, the highest peak in the Himalayas, is 8848 meters.
  3. A kite is flying at a distance of 120 meters from the ground.
  4. The tunnel is at a depth of 2 meters under the ground.

Solution:

  1. A submarine is at a depth of -512 meters from sea level.
  2. The height of Mt Everest, the highest peak in the Himalayas is +8848 meters.
  3. A kite is flying at a distance of +120 meters from the ground.
  4. The tunnel is at a depth of -2 meters from the ground.

Maharashtra Board Class 6 Maths Chapter 3 Integers Practice Set 4 Intext Questions and Activities

Question 1.
Take warm water in one beaker, some crushed ice in another and a mixture of salt and crushed ice in a third beaker. Ask your teacher for help in measuring the temperature of the substance in each of the beakers using a thermometer. Note the temperatures. (Textbook pg. no. 13)
Maharashtra Board Class 6 Maths Solutions Chapter 3 Integers Practice Set 4 1
Solution:
( Students should attempt this activity on their own)

Question 2.
Look at the picture of the kulfi man. Why do you think he keeps the kulfi moulds in a mixture of salt and ice? (Textbook pg. no. 14)
Maharashtra Board Class 6 Maths Solutions Chapter 3 Integers Practice Set 4 2
Solution:
Kulfi man keeps the kulfi moulds in a mixture of salt and ice because such a mixture helps in keeping the kulfi cool for a longer period of time. The kulfi kept in the said mixture relatively takes more time to melt. This mixture is Considered ideal as it has the temperature of -4°C as against the temperature of ice i.e. 0°C.

Question 3.
My class, i.e. Std. VI, is a part of my school. My school is in my town. My town is a part of a taluka. In the same way, the taluka is a part of a district, and the district is a part of Maharashtra State. In the same way, what can you say about these groups of numbers? Textbook pg. no. 15)
Maharashtra Board Class 6 Maths Solutions Chapter 3 Integers Practice Set 4 3
Solution:
By observing the above given groups of numbers, we can infer that natural numbers are a part of whole numbers. In turn, whole numbers are a part of integers.