Question

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

• A. 132
• B. 39
• C. 48
• D. 88

Answer 1

The correct option is C

48

Let the digits at units and tens place be x and y respectively.
$\therefore$ the number = 10y + x . . . . (i)
Number formed by interchanging the digits = 10x + y
According to the given condition, we have (10y + x) + (10x + y) = 132
and (10y + x) + 12 = 5(x + y)
$\Rightarrow$ 11x + 11y = 132 and 4x - 5y = 12
$\Rightarrow$ x + y - 12 = 0 . . . (ii) and 4x - 5y - 12 = 0 . . . (iii)
Solving these two equations:
Multiplying eq. (i) $\times$ 4, we get
4x + 4y = 48 . . . (iv)
On subtracting (iii) from (iv), we get
9y = 36
$\Rightarrow$ y = 4
Substituting y = 4 in eq. (ii), we get
x + 4 - 12 = 0
$\Rightarrow$ x = 8
$\Rightarrow$ x = 8 and y = 4
On substituting the values of x and y in equation (1), we have
10y + x = 10 $\times$ 4 + 8 = 48
$\therefore$ The number is 48.