Question

The sum of a two digit number formed by interchanging the digits is 132 if 12 is added to the number, the new number formed becomes 5 time the sum of the digits. Find the number

Answer 1

let the digit at ones place be x. thus, digit at tens place = 10x
{x + (10x)} = 132
11x = 132
NEW NO. = 11x + 12
5(11x) = 11x +12
55x = 11x +12
55x - 11x = 12
44x = 12
x = 44/12
x = 3.66

Answer 2

Let the digits of the number be X & Y

Then the number will be,

10X + Y

And the number formed by interchanging the digits will be,

10Y + X

Then according to the first condition,

(10X + Y) + ( 10Y + X) = 132

or, 11X + 11Y = 132

or, 11(X + Y) = 132

or, X + Y=132/11

∴ X + Y= 12..............................(1)

Acording to the second condition,

10X + Y + 12= 5(X + Y)

or,10X + Y + 12 = 5×12 (∵ X + Y=12)

or, 10X + Y = 60-12

∴ 10X + Y = 48...................................(2)

Subtracting (1) from (2),

9X = 36

∴ X=4

Putting X=4 in (1)

4+Y = 12

∴Y = 8

∴ The required number - 10X + Y

                                       = 40 + 8 =48