# A three-digit number 2 a 3 is added to the number 326 to give a three-digit number 5b9 which is divisible by 9. Find the value of b - a.

**Solution:**

2a3 is added to 326 as shown below and the resultant number 5b9 is divisible by 9.

2 a 3

__+3 2 6__

__5 b 9__

If 5b9 is divisible by 9 then the __sum__ of its digits should be divisible by 9.

5 + b + 9 = 14 + b is divisible by 9

For 14 + b to be divisible by 9 the minimum value of b = 4. The other values of

are b = 13, 22….. But since b is single digit these values of b are invalid.

b = 4 and therefore

b = a + 2 = 4

a =2

b - a = 4 - 2 = 2

**✦ Try This: **A three-digit number 3 a 4 is added to the number 437 to give a three-digit

number 8b1 which is divisible by 9. Find the value of a - b.

3 a 4

__+4 3 7__

8 b 1

Looking at the units place of both the three digit numbers being added we have,

4 + 7 = 11 (1 remains in the units place and 1 carries over)

Looking at the ten’s place we have

a + 1 + 3 = b

Since 7b1 is divisible by 9 then

7 + b + 1 is divisible by 9

Minimum value of b is 1 because 7+ 1 + 1 = 9 is divisible by 9

The next value of b is 10 but that is not valid because it is two digit.

Now if b = 1 then

1(from carry over) + a + 3 = 11 (1 will carry over to hundreds place)

a = 11 - 1 - 3

a = 7

a - b = 7 - 1 = 6

**☛ Also Check: **NCERT Solutions for Class 8 Maths Chapter 16

**NCERT Exemplar Class 8 Maths Chapter 13 Problem 66**

## A three-digit number 2 a 3 is added to the number 326 to give a three-digit number 5b9 which is divisible by 9. Find the value of b - a.

**Summary:**

A three-digit number 2 a 3 is added to the number 326 to give a three-digit number 5b9 which is divisible by 9, the value of b - a is 2.

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