Question

The sum of a two - digit number and the number obtained by reversing the digit is 66. If the digit of the number differ by 2 ,find the number ​

Answer 1

Given

The sum of a two - digit number and the number obtained by reversing the digit is 66. If the digit of the number differ by 2

To Find

find the number

Solution

★ Let the ten's digit be x and one's digit be y

• Required number = 10x + y
• Reversed number = 10y + x

According to the given condition

→ (10x + y) + (10y + x) = 66

→ 10x + y + 10y + x = 66

→ 11x + 11y = 66

→ 11(x + y) = 66

→ x + y = 6 ----(i)

★ The digit of the number differ by 2

→ x - y = 2 ---(ii)

Add both the equations

→ (x + y) + (x - y) = 6 + 2

→ x + y + x - y = 8

→ 2x = 8

→ x = 8/2 = 4

Putting the value of x in eqⁿ (i)

→ x + y = 6

→ 4 + y = 6

→ y = 6 - 4 = 2

Hence,

Required number = 10x + y = 42