Question

The digits of a two-digit number differ by 4. If the digits are interchanged, and the resulting number is added to the original number, we get 152. What can be the original number?

(a) 95

(b) 40

(c) 73

(d) 59

This question was posed to me by my school teacher while I was bunking the class.

My doubt is from Applications of Linear Equation (Create and Solve the Equations) topic in section Linear Equations in One Variable of Mathematics – Class 8

Answer 1

Correct answer is (a) 95

Easy explanation: Let us take the two digit number such that the digit in the units place is x. The digit in tens place differs by 4 ∴ the digit in tens place is (x + 4).

∴the two digit number obtained = [10 * (x + 4)] + [x]

∴the two digit number obtained = 10x + 40 + x

∴the two digit number obtained = 11x + 40

When the digits are interchanged we obtain the number = [10 * x] + [(x + 4)]

The new number obtained = 11x + 4

As we know the original number and the new number add up to 152.

∴ [11x + 40] + [11x + 4] = 152

∴ 22x + 44 = 152

∴ 22x = 110

∴ x = 5

The original number = [10 * ( x + 4 )] + [x]

The original number = 11x + 40

The original number = 11 * (5) + 40

The original number = 55 + 40

The original number = 95.