# Playing with Numbers-NCERT Solutions

Class VIII Math
NCERT Solution for Playing with Numbers
Exercise � 16.1
Find the values of the letters in each of the following and give reasons for the steps involved.
Ans. There are two letters whose values are to be found out. Study the addition in the ones column, i.e., from A + 5 we get 2, i.e., the number whose ones digit is 2.
For the to happen, A must be 7
(∴ A + 5 = 7 + 5 = 12).
So for the addition in tens column, we have
1 + 3 + 2 = B ⇒ B = 6
So, the puzzle has been decoded as

∴ The possible values of A and B are 7 and 6 respectively.
Ans. There are three letters whose values are to be found out. Study the addition in the ones column,
i.e., from A + 8 we get 3, i.e., the number whose ones digit is 3.
For this to happen, A must be 5
(∴ A + 8 = 5 + 8 = 13)
So for the addition in tens column, we have
1 + 4 + 9 = B ⇒ 14 = B
∴ Clearly, B is 4 and C is 1.
So the puzzle has been decoded as

∴ The possible values of A, B and C are 5, 4 and 1 respectively.
Ans. There are two letters whose values are to be found:
A and B.
Study the addition in the given puzzle.
i.e., from B + 7 we get A and from A + 3 we get 6. Possible values can be
0 + 7 = 7 i.e., A = 7 but 7 + 3 ≠ 6, so rejected
1 + 7 = 8 i.e., A = 8 but 8 + 3 ≠ 6, so rejected
2 + 7 = 9 i.e., A = 9 but 9 + 3 ≠ 6, so rejected
3 + 7 = 10 i.e., A = 0 but 1+ 0 + 3 ≠ 6, so rejected
4 + 7 = 11 i.e., A = 1 but 1 + 1 + 3 ≠ 6, so rejected
5 + 7 = 12 i.e., A = 1 but 1+ 2 + 3 ≠ 6,
So, this value of B = 5 works out correctly and B = 5 gives A as 2. So, the puzzle has been decoded as

Ans. This has two letters whose values are to be found:
A and B.
Study the addition in the tens column : from 2 + A we get 0, that is, a number whose ones digit is 0. For this to happen, the ones digit of A should be 8. And since A is a digit, we get A = 8. So, the puzzle becomes

Now, study the addition in the ones column : from 8 + B we get 9. For this to happen, we must have B = 1. Therefore, the puzzle has been decoded as