# NCERT Solutions for Class 8 Maths Maths - NCERT Solution Chapter 16

## Playing with Numbers Class 8

### Exercise 16.1 : Solutions of Questions on Page Number : 255

Q1 :

Find the values of the letters in the following and give reasons for the steps involved.

The addition of A and 5 is giving 2 i.e., a number whose ones digit is 2. This is possible only when digit A is 7. In that case, the addition of A (7) and 5 will give 12 and thus, 1 will be the carry for the next step. In the next step,

1 + 3 + 2 = 6

Therefore, the addition is as follows.

Clearly, B is 6.

Hence, A and B are 7 and 6 respectively.

Q2 :

Find the values of the letters in the following and give reasons for the steps involved.

The addition of A and 8 is giving 3 i.e., a number whose ones digit is 3. This is possible only when digit A is 5. In that case, the addition of A and 8 will give 13 and thus, 1 will be the carry for the next step. In the next step,

1 + 4 + 9 = 14

Therefore, the addition is as follows.

Clearly, B and C are 4 and 1 respectively.

Hence, A, B, and C are 5, 4, and 1 respectively.

Q3 :

Find the value of the letter in the following and give reasons for the steps involved.

Q4 :

Find the values of the letters in the following and give reasons for the steps involved.

Q5 :

Find the values of the letters in the following and give reasons for the steps involved.

Q6 :

Find the values of the letters in the following and give reasons for the steps involved.

Q7 :

Find the values of the letters in the following and give reasons for the steps involved.

Q8 :

Find the values of the letters in the following and give reasons for the steps involved.

Q9 :

Find the values of the letters in the following and give reasons for the steps involved.

Q10 :

Find the values of the letters in the following and give reasons for the steps involved.

### Exercise 16.2 : Solutions of Questions on Page Number : 260

Q1 :

If 21y5 is a multiple of 9, where y is a digit, what is the value of y?

Q2 :

If 31z5 is a multiple of 9, where z is a digit, what is the value of z?

You will find that there are two answers for the last problem. Why is this so?

Q3 :

If 24x is a multiple of 3, where x is a digit, what is the value of x?

(Since 24x is a multiple of 3, its sum of digits 6 + x is a multiple of 3; so 6 + x is one of these numbers: 0, 3, 6, 9, 12, 15, 18…. But since x is a digit, it can only be that 6 + x = 6 or 9 or 12 or 15. Therefore, x = 0 or 3 or 6 or 9. Thus, x can have any of four different values)