CG Board Class 10 Maths Chapter 5 Solutions: Ratio and Proportion (अनुपात एवं समानुपात) (2026-27)

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CG Board (CGBSE / SCERT Chhattisgarh) Class 10 Mathematics Solutions | 2026-27 Edition

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📚 Chapter Overview:

  • Board: Chhattisgarh Board of Secondary Education (CGBSE) / CG SCERT Raipur
  • Subject & Unit: Class 10 Mathematics – Unit 1: Algebra (2026-27 Edition)
  • Chapter 5: Ratio and Proportion (अनुपात एवं समानुपात)
  • Medium: Bilingual Step-by-Step Solutions (English Medium + हिंदी माध्यम)
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Official Textbook Exercises

End-of-Chapter Exercises (Solutions)

Question 1

*Ratio A relationship between two quantities of the same uni…


📝 Question:

  • *Ratio

A relationship between two quantities of the same unit showing how many times one quantity is of the other. It is represented as a : b or a/b.

  • *Comparison of Ratios

To compare ratios, either make their denominators equal or convert them into percentages.

  • *Proportion

When two ratios are equal, they are said to be in proportion.

a : b :: c : d ⇒ a/b = c/d

  • a, d are called Extreme terms.
  • b, c are called Middle terms.
  • *Property: Product of Extremes = Product of Middles

a · d = b · c

  • *Fourth Proportional

If a, b, c, x are in proportion (a : b :: c : x), then fourth proportional x = (b · c)/(a).

  • *Continued Proportion

If three quantities a, b, c are in continued proportion, then a : b :: b : c ⇒ a/b = b/c ⇒ b2 = ac.

  • b = √ac is called the *Mean Proportional of a and c.
  • c = b2/a is called the *Third Proportional of a and b.
  • *Direct and Inverse Proportion
  • *Direct Proportion: Increasing one quantity causes a proportional increase in the other (x/y = k).
  • *Inverse Proportion: Increasing one quantity causes a proportional decrease in the other (x · y = k).
💡 Solution:

Question 2

In a cricket match batsman Dheerendra scores 19…


📝 Question:

In a cricket match, batsman Dheerendra scores 19 runs in 25 balls and gets out, Mahendra scores 14 runs in 19 balls and is sent back to the pavilion and Ravindra scores 9 runs in 16 balls. Who scored fastest and who was the slowest?

💡 Solution:

Dheerendra scored fastest and Ravindra was the slowest.*

Question 3

In a 100 m race Ram runs at…


📝 Question:

In a 100 m race, Ram runs at a speed of 12 km per hour leaving Shyam 5 meters behind. What was Shyam’s speed?

💡 Solution:

11.4 km/hour*

Question 4

The volume of salt water on earth is…


📝 Question:

The volume of salt water on earth is 38214 million cubic kilometers and that of fresh water is 1386 million cubic kilometers. Tell the ratio of fresh water to salt water on earth? What is the percentage of fresh water on earth? And the percentage of salt water?

💡 Solution:

Ratio = 7:193; Fresh water = 3.5%, Salt water = 96.5%**

Question 5

Mahesh cuts the paddy crop in a field…


📝 Question:

Mahesh cuts the paddy crop in a field in 12 days. Gayatri cuts the same crop in 9 days. How many days would be needed to cut the crop if they both work together?

💡 Solution:

51/7 days*

Question 6

What needs to be added to 55 127…


📝 Question:

What needs to be added to 55, 127, 68 and 153 so that they become proportional?

💡 Solution:

1 (or 17 based on question parameters)**

Question 7

If 12 labourers complete a work in 16…


📝 Question:

If 12 labourers complete a work in 16 days, in how many days can 4 labourers complete the same work?

💡 Solution:

48 days*

Question 8

Divide Rs 364 among three persons in the…


📝 Question:

Divide Rs. 364 among three persons in the ratio 1:2:4

💡 Solution:

Rs. 52, Rs. 104, Rs. 208*

Question 9

Find a b c if a b 2…


📝 Question:

Find a : b : c if a : b = 2 : 3 and b : c = 5 : 8

💡 Solution:

10:15:24*

Question 10

Three persons earn a profit of Rs 70000…


📝 Question:

Three persons earn a profit of Rs. 70,000 in a business which they divide in ratio A:B = 4:2 and B:C = 10:5. How much money will each person get? The money received by A would be how many times the money received by C?

💡 Solution:

A = Rs. 40,000, B = Rs. 20,000, C = Rs. 10,000; 4 times*

Question 11

A bag contains Rs 1 Rs 2 and…


📝 Question:

A bag contains Rs. 1, Rs. 2 and Rs. 5 coins in the ratio 1:2:5. If the total money in the bag is Rs. 1590, find the number of each type of coin

💡 Solution:

53, 106, 265 coins**

Question 12

We have 100 liters of a mixture of…


📝 Question:

We have 100 liters of a mixture of milk and water which is 10% water. How much more pure milk should be added so that the new mixture has only 5% water?

💡 Solution:

100 liters (or 4 liters as per textbook key variant)**

Question 13

Find the fourth proportional of 7 11 14


📝 Question:

Find the fourth proportional of 7, 11, 14

💡 Solution:

22*

Question 14

Find the mean proportional of 2xsup2sup y and…


📝 Question:

Find the mean proportional of 2x2 y and 8y3

💡 Solution:

4xy2**

Question 15

Find the third proportional of xsup2sup ysup2sup and…


📝 Question:

Find the third proportional of x2 – y2 and x – y

💡 Solution:

(x – y)/(x + y)**

Question 16

What number should be added to 10 18…


📝 Question:

What number should be added to 10, 18, 22, 38 so that they become proportional?

💡 Solution:

2**

Question 17

If b is the mean proportional of a…


📝 Question:

. If b is the mean proportional of a and c, prove that (a2 + b2)/(ab) = (a + c)/(b).**

💡 Solution:

/(ab) = (a + c)/(b))*

  • Proof /

Given b2 = ac.

LHS = (a2 + b2)/(ab) = (a2 + ac)/(ab) = (a(a + c))/(ab) = (a + c)/(b) = RHS

Question 18

Find two numbers such that their mean proportional…


📝 Question:

Find two numbers such that their mean proportional is 24 and third proportional is 192

💡 Solution:

12 and 48*

Question 19

If a b c d then prove that…


📝 Question:

. If a : b = c : d, then prove that (a2 + c2)/(b2 + d2) = ac/bd.**

💡 Solution:

/(b2 + d2) = ac/bd)*

  • Proof /

Let a/b = c/d = k ⇒ a = bk, c = dk.

LHS = (b2 k2 + d2 k2)/(b2 + d2) = (k2 (b2 + d2))/(b2 + d2) = k2

RHS = ((bk)(dk))/(bd) = (bd k2)/(bd) = k2

Since LHS = RHS = k2, it is proved.

Question 20

If x y a b then prove that…


📝 Question:

. If x : y = a : b, then prove that (x2 + y2)/(a2 + b2) = xy/ab.**

💡 Solution:

/(a2 + b2) = xy/ab)*

  • Proof /

Let x/a = y/b = k ⇒ x = ak, y = bk.

LHS = (a2 k2 + b2 k2)/(a2 + b2) = k2

RHS = ((ak)(bk))/(ab) = k2

Since LHS = RHS = k2, it is proved.

Question 21

A task is completed by 45 labourers in…


📝 Question:

A task is completed by 45 labourers in 24 days if they work 6 hours per day. How many labourers will be needed to complete the task in 15 days if they work for 8 hours every day?

💡 Solution:

54 labourers*

Question 22

A task is completed by 25 persons in…


📝 Question:

A task is completed by 25 persons in 9 days if they work 6 hours per day. How many days will be needed to complete the task if 15 persons work for 9 hours every day?

💡 Solution:

10 days*

Question 23

A task is completed by 30 persons in…


📝 Question:

A task is completed by 30 persons in 15 days if they work 6 hours per day. How many hours of work will be needed every day if 20 persons have to complete it in 15 days?

💡 Solution:

9 hours/day*

Question 24

A car leaves Saraipalli travels at 75 km…


📝 Question:

A car leaves Saraipalli, travels at 75 km per hour and reaches Raipur in 4 hours. The next time there was traffic and construction work on the road due to which the speed is decreased by 15 km per hour. How long will the car take to reach Raipur?

💡 Solution:

5 hours*

Question 25

If 10 bulbs are lighted 4 hours every…


📝 Question:

If 10 bulbs are lighted 4 hours every day for 60 days then the electricity bill is Rs. 80. How many bulbs can be lighted for 3 hours every day for 16 days so that the electricity bill is Rs. 40?

💡 Solution:

25 bulbs*

Question 26

A task is completed by 48 persons in…


📝 Question:

A task is completed by 48 persons in 25 days if they work 8 hours per day. How many days will be needed to complete double the task if 30 persons work for 10 hours every day?

💡 Solution:

64 days*

Question 27

A and B together complete a task in…


📝 Question:

A and B together complete a task in 24 days, C and B together complete the same task in 18 days, and A and C together complete the task in 12 days. How many days will A take to complete the task if he works alone?

💡 Solution:

284/5 days*

Question 28

A task is completed by 15 men in…


📝 Question:

A task is completed by 15 men in 16 days. How many men will be needed to complete 1/4th of the task in 15 days?

💡 Solution:

4 men / persons*

Question 29

A camp has sufficient provisions for 120 soldiers…


📝 Question:

A camp has sufficient provisions for 120 soldiers. If after 40 days, 40 soldiers were deputed elsewhere, how long will the remaining provisions last for the remaining soldiers?

💡 Solution:

30 days*

Question 30

An open pipe takes 15 hours to fill…


📝 Question:

An open pipe takes 15 hours to fill a tank. Due to a leak, it takes 20 hours. How long will the leak take to empty the full tank?

💡 Solution:

60 hours / 11 days*

Question 31

Three taps A B and C can fill…


📝 Question:

Three taps A, B and C can fill or empty a tank in 30, 40 and 60 minutes respectively (A, B fill, C empties). If all three taps are opened together, how long will it take to fill the tank?

💡 Solution:

24 minutes / 15 hours*

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