Question

A number consisting of two digits is seven times the sum of its digits. When 27 is subtracted from the number, the digits are reversed. Find the number.

Answer 1

Let the tens and the units digits of the required number be x and y, respectively.
Required number = (10x + y)
10x + y = 7(x + y)
10x + 7y = 7x + 7y or 3x – 6y = 0                   ……….(i)
Number obtained on reversing its digits = (10y + x)
(10x + y) - 27 = (10y + x)
⇒10x – x + y – 10y = 27
⇒9x – 9y = 27
⇒9(x – y) = 27
⇒x – y = 3                           ……..(ii)
On multiplying (ii) by 6, we get:
6x – 6y = 18                  ………(iii)
On subtracting (i) from (ii), we get:
3x = 18
⇒ x = 6
On substituting x = 6 in (i) we get
3 × 6 – 6y = 0
⇒ 18 – 6y = 0
⇒ 6y = 18
⇒ y = 3
Number = (10x + y) = 10 × 6 + 3 = 60 + 3 = 63
Hence, the required number is 63.