Question

A two digit no. is seven times the sum of its digit. The no. Formed by reversing the digit less is18 less than the given no. .Find the given no.

Answer 1

Hey

Here is your answer,

Let the digits in ones place be x and ten’s place be y
The original number = 10y + x
Number formed by interchanging the digits = 10x + y

Given (10y + x) = 7(x + y)
10y + x = 7x + 7y
7x + 7y – x – 10y = 0
6x – 3y = 0
2x – y = 0 → (1)

It is also given that on reversing the digits the number obtained is 18 less than the original number
Hence 10x + y = (10y + x) – 18
10x + y – 10y – x = – 18
9x – 9y = – 18
x – y = – 2 → (2)

Subtract (2) from (1)
2x – y = 0
x – y = – 2
-------------
x = 2

Put x = 2 in 2x – y = 0
2(2) – y = 0
∴ y = 4

Therefore the original number is 42.

Hope it helps you!