Question

Seven times a two digit number is equal to four times the number obtained by reversing the digits. If the difference between the digits is 3 find the number.

Answer 1

Let the digit at ten’s place be x and the digit at unit’s place be y.

Required number = 10y + x

When the digits are interchanged,

Reversed number = 10x + y

7(10y + x) = 4(10x + y)

∴ 70y + 7x = 40x + 4y

7x - 40x = 4y - 70y 

-33x = -66y

x = `(66y)/33`

x = 2y      ...(1)

x - y = 3        ...(2)

From equation (1) & (2)

2y - y = 3

y = 3

From equation (1)

x = 2(3)

x = 6

Thus, Required number = 10(3) + 6 = 36