#### Question

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

A B

+ 3 7

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6 A

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#### Solution

The addition of A and 3 is giving 6. There can be two cases.

1) **First step is not producing a carry**

In that case, A comes to be 3 as 3 + 3 = 6. Considering the first step in which the addition of B and 7 is giving A (i.e., 3), B should be a number such that the units digit of this addition comes to be 3. It is possible only when B = 6. In this case, A = 6 + 7 = 13. However, A is a single digit number. Hence, it is not possible.

2) **First step is producing a carry**

In that case, A comes to be 2 as 1 + 2 + 3 = 6. Considering the first step in which the addition of B and 7 is giving A (i.e., 2), B should be a number such that the units digit of this addition comes to be 2. It is possible only when B = 5 and 5 + 7 = 12.

2 5

+ 3 7

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6 2

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Hence, the values of A and B are 2 and 5 respectively.