RD Sharma Class 8 Maths Solutions Chapter 5- Playing with Numbers (2025-26)

Get complete RD Sharma Solutions for Class 8 Maths Chapter 5- Playing with Numbers here. The solutions are solved by expert teachers, making each answer simple and easy to understand. You’ll also find shortcut tips and practical examples to help you quickly solve all the exercise questions.

Practising these RD Sharma solutions class 8 regularly will help you score good marks in your exams by building a strong understanding of the concepts.

What’s Covered in Chapter 5 – Playing with Numbers?

This chapter has three exercises, and our RD Sharma solutions provide clear answers for every question. Important topics explained in this chapter include:

• How to interchange digits in a number
• Writing numbers in their general form
• Divisibility tests for numbers like 10, 5, 2, 9, 3, 6, 11, and 4
• Solving interesting number puzzles called Cryptarithms

These solutions make Maths more fun and simple, helping students to understand each concept in an easy way.

RD Sharma Class 8 Maths Solutions Chapter 5 - Playing With Numbers Download PDF

Home-Tution provide step-by-step solutions for all exercise questions from Class 8 RD Sharma Chapter 5 – Playing With Numbers are available here. You can easily find all the exercises with detailed solutions for Chapter 5 – Playing With Numbers listed below.

Access Answers to Maths RD Sharma Solutions for Class 8 Chapter 5

Q. Without performing actual computations, find the quotient when 94-49 is divided by

(i) 9 

(ii) 5

Solution:

Step 1: Simplify the Expression (94 - 49)

94 - 49 = 45

So, we need to divide 45 by 9 and by 5.

(i) 45 ÷ 9

We know the multiplication table of 9:

9 × 5 = 45

Quotient = 5

(ii) 45 ÷ 5

From the 5 times table:

5 × 9 = 45

Quotient = 9

Final Answer:

• (i) Quotient = 5
• (ii) Quotient = 9

Q. Without performing actual addition and division, write the quotient when the sum of 69 and 96 is divided by

(i) 11 

(ii) 15

Solution:

(i) Division by 11

Numbers 69 and 96 have their digits reversed (the tens and units places are interchanged).

The sum of the digits is:

6 + 9 = 15

It is known that when we add such numbers (69 + 96) and divide the result by 11, the quotient equals the sum of the digits.

So, (69 + 96) ÷ 11 = 15

(ii) Division by 15

Again, for 69 and 96, the digits are reversed.

The sum of the digits remains 6 + 9 = 15

This time, when we divide (69 + 96) by 15 (the sum of digits), the quotient becomes 11.

So, (69 + 96) ÷ 15 = 11

Q. If the sum of the number 985 and two other numbers obtained by arranging the digits of 985 in cyclic order is divided by 111, 22 and 37, respectively. Find the quotient in each case.

Solution: The given numbers are 985, 859, and 598.

These numbers are written in cyclic order (rotating their digits). We know that when the sum of such three-digit numbers is divided by 111, the quotient equals the sum of the digits.

Sum of digits = 9 + 8 + 5 = 22

Therefore,

(985 + 859 + 598) ÷ 111 = 22

When the sum of numbers is divided by the sum of digits (22), the quotient becomes 111.

So, (985 + 859 + 598) ÷ 22 = 111

We also know:

3 × 37 = 111

So, the quotient can also be expressed as:

Quotient = 3 × Sum of digits = 3 × 22 = 66

Q. Find the quotient when the difference between 985 and 958 is divided by 9.

Solution: The difference between 985 and 958 involves swapping the ten’s and unit’s digits.

We know that when we interchange the ten’s and unit’s place, the difference between the two numbers is always divisible by 9, and the quotient equals the difference between the digits in the ten’s and unit’s place.

Difference = 8 – 5 = 3

Quotient = 3

Q. Find the remainder when 981547 is divided by 5. Do that without doing actual division.

Solution: We know that when any number is divided by 5, the remainder depends only on the unit digit.

The last digit of 981547 is 7.

7 ÷ 5 = 1 remainder 2

Therefore, when 981547 is divided by 5, the remainder is 2.

For the quotient, we ignore the remainder and divide fully.

Since 7 ÷ 5 = 1 remainder 2, we subtract the remainder and divide the rest.

Quotient = (981547 - 2) ÷ 5 = 981545 ÷ 5 = 196309

Final Answer:

• Remainder = 2
• Quotient = 196309

Q. Find the remainder when 51439786 is divided by 3. Do that without performing actual division.

Solution: We know that when a number is divided by 3, the remainder is the same as the remainder obtained by dividing the sum of its digits by 3.

Here, the number is 51439786.

Sum of digits = 5 + 1 + 4 + 3 + 9 + 7 + 8 + 6 = 43

Now, 43 ÷ 3 = 14 remainder 1

Therefore, when 51439786 is divided by 3, the remainder is 1.

Q. Without performing actual division, find the remainder when 928174653 is divided by 11.

Solution: We know that when a number is divided by 11, the remainder is found by taking the difference between the sum of digits at odd and even places.

9, 2, 8, 1, 7, 4, 6, 5, 3

Odd places (1st, 3rd, 5th, 7th, 9th): 9 + 8 + 7 + 6 + 3 = 33

Even places (2nd, 4th, 6th, 8th): 2 + 1 + 4 + 5 = 12

33 – 12 = 21

21 ÷ 11 leaves a remainder of 10.

Final Answer: The remainder when 928174653 is divided by 11 is 10.

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