Question

The sum of a two-digit number and the number

obtained by reversing its digits is 132. The fraction
formed by taking three less than the number as
numerator and six more than the number formed by
reversing its digits as denominator is 2/3.What is the
number?

Answer 1

57

Explanation:

Let x = the tens digit of the original number, and

y = the ones digit...

Therefore, the general form of the number is 10x + y

2 Unknowns requires 2 equations:

(10x + y) + (10y + x) = 132

`(10x+y-3)/(10y+x+6)=(2)/(3)`

Simplify each equation and Solve the system:

(10x + y) + (10y + x) = 132 ⇒ 11x + 11y = 132 ⇒ x + y = 12 ⇒ y = 12 - x

`(10x+y-3)/(10y+x+6)=(2)/(3)` ⇒ 30x + 3y - 9 = 20y + 2x + 12 ⇒ 28x - 17y = 21

⇒ 28x - 17(12 - x) = 21

⇒ 28x - 204 + 17x = 21

⇒ 45x = 225

⇒ x = 5

y = 12 - x ⇒ y = 7

Check: 57 + 75 = 132