Playing with Numbers-NCERT Solutions

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