# A two digit number is three times the sum of its digits. If 45 is added to it, the digits are reversed. The number is

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A two digit number is three times the sum of its digits. If 45 is added to it, the digits are reversed. The number is

( A ) 32  ( B ) 27  ( C ) 23  ( D ) 72

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The correct option is (B) 27.

Explanation:

Let the tens and the units digits of the required number be x and y, respectively.

Let the number be 10x + y.

Now,

10x + y = 3(x +y)

10x + y = 3x + 3y

10x - 3x = 3y - y

7x = 2y

7x - 2y = 0 .........(i)

Given that if 45 is added to it, the digits are reversed.

(10x + y)+ 45 = (10y + x)

10x + y + 45 = 10y + x

10x - x + y - 10y = -45

9x - 9y = -45

9(x - y) = -45

x - y = -45/9

x - y = -5 .........(ii)

Multiplying (i) by 1 and (ii) by 2, we gets

7x - 2y = 0 ………(iii)

2x - 2y = -10  ……..(iv)

Subtracting (iv) from (iii), we get

7x – 2x = 10

5x = 10

x = 10/5 = 2

Putting x = 2 in (i), we get

7x - 2y = 0

7 x 2 - 2y = 0

14 - 2y = 0

-2y = -14

y = -14/-2 = 7

Number = (10x + y)

= 10 x 2 + 7

= 20 + 7

= 27

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Solution: Correct answer is ( B ) 27

Explanation:

From the options take 27 sum of digits = > 2+7=9
times the sum of its digits = 3*9= 27
45 is added we get 72
if digits are reversed we get 27

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