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Mathematics

In each of the following cases, find the least value/values of letters used in place of digits :

3A+25B2\begin{matrix} & 3 & \text{A} \ + & 2 & 5 \ \hline & \text{B} & 2 \ \hline \end{matrix}

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3A+25B2\begin{matrix} & 3 & \text{A} \ + & 2 & 5 \ \hline & \text{B} & 2 \ \hline \end{matrix}

Clearly, A + 5 is a number whose ones digit is 2.

⇒ A + 5 = 2, A + 5 = 12, A + 5 = 22; and so on.

⇒ A = 2 - 5, A = 12 - 5, A = 22 - 5; and so on.

⇒ A = -3, A = 7, A = 17; and so on.

As A is a digit, so A = 7.

317+25B2\begin{matrix} & \overset{1}{3} & \text{7} \ + & 2 & 5 \ \hline & \text{B} & 2 \ \hline \end{matrix}

Now, finding the value of B.

1 + 3 + 2 = B

6 = 5

Since, A is a digit. ∴ A = 7, B = 6.

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