Question

8 times a two digit number is equal to 3 times the number obtained by reversing the order of its digits. If difference between the digit 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