Question

The sum of two digit number formed by interchanging the digit is 132 if 12 is added to the number the new number become 5 times the sum of digits

Answer 1

Answer:

48

Step-by-step explanation:

Let say two digits number = xy

Value of number = 10x + y

Interchanged number = yx

Value of interchanged number = 10y + x

Number + interchanged number = 132

10x + y + 10y + x = 132

11x + 11y = 11×12

x + y = 12    EQ 1

Sum of two digits = x + y

so sum of digits = 12 from EQ 1

12 is added to number  = 5 × Sum of Digits

10x + y + 12 = 5 × 12

10 x + y = 48  EQ 2

EQ 2 - EQ 1

10x + y - x - y = 48 -12

9x = 36

x = 4

4 + y = 12

y = 8

number = 48

Answer 2

Answer:

Let the number be xy = 10x + y

Number obtained by interchanging the digits = yx = 10y + x

From the given information, we have:

10x + y + 10y + x = 132 11x + 11y = 132 x + y = 12 ... (1)

Also, we have:

10x + y + 12 = 5(x + y) 10x + y + 12 - 5x - 5y = 0 5x - 4y + 12 = 0 ... (2)

Multiplying (1) by 4, we get 4x + 4y - 48 = 0 ...

(3) Adding (2) and (3), we get, 9x - 36 = 0 x = 4 So, y = 12 - 4 = 8

Thus, the number is 48.

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