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10
NCERT Solutions · Maths Ch 10
Proportional Reasoning-2
22 questions · 4 exercises
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Ex 10.1
Ex 10.2
Ex 10.3
Ex 10.4
NCERT answers with full exam-style working, step by step. Tap a question to open its solution.
1
EXERCISE 10.1 · 5 QUESTIONS
Ratios of many quantities
Q1
A cricket coach schedules practice in the ratio warm-up/cool-down : batting : bowling : fielding :: 3 : 4 : 3 : 5. If each session is 150 minutes long, how much time is spent on each activity?
(3 marks)
Q2
The books in a school library are in the ratio Odiya : Hindi : English :: 3 : 2 : 1. If the library has 288 Odiya books, how many Hindi and English books does it have?
(2 marks)
Q3
I have 100 coins in the ratio ₹10 : ₹5 : ₹2 : ₹1 coins :: 4 : 3 : 2 : 1. How much money do I have in coins?
(3 marks)
Q4
Construct a triangle with side lengths in the ratio 3 : 4 : 5. Will all the triangles drawn with this ratio of side lengths be congruent to each other? Why or why not?
(3 marks)
Q5
Can you construct a triangle with side lengths in the ratio 1 : 3 : 5? Why or why not?
(2 marks)
2
EXERCISE 10.2 · 3 QUESTIONS
Pie charts
Q1
A group of 360 people voted for their favourite season: 90 liked summer, 120 liked rainy, the rest liked winter. Draw a pie chart.
(3 marks)
Q2
Draw a pie chart for viewers' favourite TV channel: Entertainment 50%, Sports 25%, News 15%, Information 10%.
(2 marks)
Q3
Prepare a pie chart that shows the favourite subjects of the students in your class (use the data of your own class).
(2 marks)
3
EXERCISE 10.3 · 2 QUESTIONS
Inverse proportion (tables)
Q1
Which of these are in inverse proportion? (i) x: 40, 80, 25, 16; y: 20, 10, 32, 50 (ii) x: 40, 80, 25, 16; y: 20, 10, 12.5, 8 (iii) x: 30, 90, 150, 10; y: 15, 5, 3, 45
(3 marks)
Q2
Fill in the empty cells if x and y are in inverse proportion. x: 16, 12, __, 36; y: 9, __, 48, __ (the second y and the third x and fourth y are empty).
(3 marks)
4
EXERCISE 10.4 · 12 QUESTIONS
Inverse proportion (problems)
Q1
Which pairs of quantities are in inverse proportion? (i) number of taps filling a tank and time taken (ii) number of painters and days needed to paint a wall (iii) distance a car can travel and petrol in the tank (iv) speed of a cyclist and time for a fixed route (v) length of cloth bought and price at a fixed rate (vi) number of pages in a book and time to read it at fixed speed
(2 marks)
Q2
If 24 pencils cost ₹120, how much will 20 such pencils cost?
(2 marks)
Q3
A tank has enough water for 20 families for 6 days. If 10 more families move in, how long will the water last? What assumptions do you need?
(2 marks)
Q4
Fill in the average hours each living being sleeps in a day from the charts (options: 15, 2.5, 20, 8, 3.5, 13, 10.5, 18).
Figure: eight ring charts with the sleeping part shown in blue: giraffe (about 10%), elephant (about 15%), human (about 33%), dog (about 44%), cat (about 54%), squirrel (about 62%), snake (about 75%), bat (about 83%).
(3 marks)
Q5
The pie chart shows the modes of transport used by children to go to school: Walk 90°, Bus 120°, Two-wheeler 60°, Cycle 60°, Car (the remaining slice). (i) What is the most common mode? (ii) What fraction travel by car? (iii) If 18 children travel by car, how many children took part? How many use taxis? (iv) By which two modes are equal numbers of children travelling?
(3 marks)
Q6
Three workers can paint a fence in 4 days. If one more worker joins the team, how many days will it take them to finish the work? What are the assumptions?
(2 marks)
Q7
It takes 6 hours to fill 2 tanks of the same size with a pump. How long will it take to fill 5 such tanks with the same pump?
(2 marks)
Q8
Chairs are arranged in 25 rows with 12 chairs in each row. If rearranged with 20 chairs in each row, how many rows are there?
(2 marks)
Q9
A school has 8 periods a day, each of 45 minutes. How long is each period if the school has 9 periods a day, with the same number of school hours per day?
(2 marks)
Q10
A small pump can fill a tank in 3 hours, a large pump in 2 hours. If both pumps are used together, how long will the tank take to fill?
(3 marks)
Q11
A factory requires 42 machines to produce a given number of toys in 63 days. How many machines are required to produce the same number of toys in 54 days?
(2 marks)
Q12
A car takes 2 hours to reach a destination at 60 km/h. How long will it take at 80 km/h?
(2 marks)