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

If the ten’s place digit is x and the digit at the unit’s place is y.

Then the required number = 10x + y 

Reversed number = 10y + x

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