Question

Eight times a two digit number is equal to three times the number obtained by reversing the order of the digits. If the difference between the digits of the number is 5, find the number

Answer 1

Let the digit in the ones place be y and tens place be x
Therefore the number = 10x + y
Number formed by reversing the digits = 10y + x
Given 8(10x + y) = 3(10y + x)
⇒ 80x + 8y = 30y + 3x
⇒ 77x – 22y = 0
∴ 7x – 2y = 0 → (1)
It is also given that the difference between the digits is 5.
Hence (y – x) = 5
– x + y = 5 → (2)
Multiply equation(2) with 2 and add to equation (1), we get
7x – 2y = 0
–2x + 2y = 10
----------------
5x = 10
∴ x = 2
Put x = 2 in – x + y = 5, we get
– 2 + y = 5
⇒ y = 7
Hence the number = (10x + y)
= (10×2 + 7)
= 27