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1. A certain number of two digits is three times the sum of its digits and if 45 be added to it, the digits are reversed. The number is ?

A. 23

B. 27

C. 32

D. 72

Solution:

Let the ten's digit be x and unit's digit be y
Then,

\begin{aligned} \Rightarrow 10 x + y = 3 (x + y) \\ \Rightarrow 7 x - 2 y = 0..... (i) \\ 10 x + y + 45 = 10 y + x \\ \Rightarrow y - x = 5..... (i i) \end{aligned}

Solving (i) and (ii), we get :
x = 2 and y = 7
∴ Required number = 27

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