Question

Mahesh’s age is a two-digit number. The peculiarity of the number is that when divided by the sum of its digits, the quotient is 2 and the remainder is 8. If the digits are interchanged and the resulting number is divided by the sum of its digits, the quotient is 8 and the remainder is 2. What is Mahesh’s age?

• A. 28
• B. 46
• C. 55
• D. 64
• E. 82

Answer 1

The Correct Option is A

We need to determine Mahesh's age based on the given peculiarities of the number.

Let's denote Mahesh's age as a two-digit number: \(10x + y\), where \(x\) is the tens digit and \(y\) is the units digit. 

According to the problem, when the number is divided by the sum of its digits, the quotient is 2 and the remainder is 8. Mathematically, this can be expressed as:

\((10x + y) = 2(x + y) + 8\)

Simplifying the equation:

\((10x + y) - 2(x + y) = 8\)

\[8x - y = 8\] (Equation 1)

Next, when the digits are reversed, the number becomes \(10y + x\). Dividing it by the sum of its digits gives a quotient of 8 and a remainder of 2:

\((10y + x) = 8(x + y) + 2\)

Simplifying the equation:

\((10y + x) - 8(x + y) = 2\)

\[2y - 7x = 2\] (Equation 2)

Now, we solve these two equations (Equations 1 and 2):

1. From Equation 1: \(y = 8x - 8\)
2. Substitute \(y\) from Equation 1 into Equation 2:

2(8x - 8) - 7x = 2

Simplify:

16x - 16 - 7x = 2

Further simplification gives:

9x = 18

Solving for \(x\):

x = 2

Substitute \(x\) back into the expression for \(y\):

y = 8(2) - 8 = 8

Thus, Mahesh's age is \(10x + y = 10 \times 2 + 8 = 28\).

Therefore, the correct answer is 28.