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.