## RS Aggarwal Class 8 solutions Chapter 5 Playing with Numbers Ex 5A in pdf free download

Contents

**Question 1.**

**The units digit of a two-digit number is 3 and seven times the sum of the digits is the number itself. Find the number.**

**Solution:**

Let tens digit = x

Units digit = 3

∴Number = 3 + 10x

According to the condition,

7 (x + 3) = 3 + 10x

7x + 21 = 3 + 10x

21 – 3 = 10x – 7x

=> 3x = 18

x =

∴Number = 3 + 10x

= 3 + 10 x 6 = 3 + 60 = 63

**Question 2.**

**In a two-digit number, the digit at the units place is double the digit in the tens place. The number exceeds the sum of its digits by 18. Find the number.**

**Solution:**

Let ten’s digit = x

Then units digit = 2x

and number = 10x + 2x = 12x

According to the condition,

12x = x + 2x + 18

12x – x – 2x = 18

=> 9x = 18

x = = 2

∴Number = 12x = 2 x 12 = 24

**Question 3.**

**A two-digit number is 3 more than 4 times the sum of its digit. If 18 is added to the number, its digits are reversed. Find the number.**

**Solution:**

Let units digit = x

and tens digit = y

Number = x + 10y

Now x + 10y = 4 (x + y) + 3

=> x + 10y = 4x + 4y + 3

10y – 4y – 4x + x = 3

=> 6y – 3x = 3

2y – x = 1 ….(i)

∴Number by reversing the order of digits = y + 10x

=>x + 10y + 18 = y + 10x

=>10x – x + y – 10y = 18

=> 9x – 9y = 18

x – y = 2 ….(ii)

∴Adding (i) and (ii)

=> 2y – y = 3

y = 3

x = 2y – 1 = 2 x 3 – 1 = 6 – 1 = 5

∴Number = x + 10y = 5 + 3 x 10

= 5 + 30 = 35

**Question 4.**

**The sum of die digits of a two-digit number is 15. The number obtained by interchanging its digits exceeds the given number by 9. Find the original number.**

**Solution:**

Sum of two digits of a number =15

Let units digit = x

Then tens digit = 15 – x

∴Number = 10 (15 – x) + x

= 150 – 10x + x = 150 – 9x

By interchanging the digits, the new number will be

= 10x + 15 – x = 9x + 15

According to the condition,

9x + 15 = 9 + 150 – 9x

9x + 9x = 159-15 = 144

18x = 144

=>x = = 8

∴Number = 150 – 9x = 150 – 9 x 8

= 150 – 72 = 78

**Question 5.**

**The difference between a 2-digit number and the number obtained by inter-changing its digits is 63. What is the difference between the digits of the number?**

**Solution:**

Let units place digit = x

and tens place digit = y

Then number = x + 10y

By interchanging the positions of the digits then

Units digits = y

and tens digit = x

∴Number = y + 10x

(x + 10y) – (y + 10x) = 63

=> x + 10y – y – 10x = 63

9y – 9x = 63

=> 9(y – x) = 63

y – x = = 7

∴Hence, difference of its digits = 7 Ans.

**Question 6.**

**In a 3-digit number, the tens digit is thrice the units digit and the hundreds digit is four times the units digit. Also, the sum of its digits is 16. Find the number.**

**Solution:**

Sum of three digits of a number = 16

Let units digit of a three-digit number = x

Then tens digit = 3x

and hundreds digit = 4x

∴Number = x + 10 x 3x + 100 x 4x

= x + 30x + 400x = 431x

But x + 3x + 4x = 16 => 8x = 16

∴x = = 2

∴Number = 431 x 862

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