Question

The sum of a 2 digit number and the number formed by interchanging the digit is 110.If 10 is subtracted from the first ,the new number is 4 more than 5 times the sum of the digits in the first number .Find the first number

Answer 1

Sol:
Let the two digit number be 10x + y
Number formed by interchanging the digits = 10y + x
According to the question, 10x + y + 10y + x = 110
⇒ x + y = 10 ------------------ (1)

10 is subtracted from the first number, the new number is 4 more than 5 times the sum of the digits in the first number
⇒ (10x + y - 10) = 5(x + y) + 4
⇒ 10x + y - 10 = 5x + 5y + 4
⇒ 5x - 4y = 14 --------------- (2)
Solving equations 1 and 2, we get
x = 6 and y = 4
Therefore, the first number is 10(6) + 4 i.e. 64.