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4.One of the two digits of a two digit number is three times the other digit. If you interchange the digits of this two-digit number and add the resulting number to the original number, you get 88. What is the original number?


Answer :

Let unit place digit be x.
And the ten’s place digit be y= 3x

Original number = x + 3x × 10 = x + 30x = 31x

Condition I: 10x + 3x = 13x [interchanging the digits]

Condition II: New number + original number = 88

13x + 31x = 88

\(\Rightarrow\) 44x = 88

\(\Rightarrow\) x = 88 ÷ 44 [Transposing 44 to RHS]

\(\Rightarrow\) x = 2

Thus, we have,

The original number = 31x = 31 × 2 = 62

Hence the required number = 62

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