The correct answer is option (A):
28
Let's break down this word problem step by step to find Mahesh's age. We'll use algebra to represent the problem.
Let Mahesh's age be represented by the two-digit number 10x + y, where 'x' is the tens digit and 'y' is the units digit.
The sum of the digits is x + y.
From the first condition, when the number is divided by the sum of its digits, the quotient is 2 and the remainder is 8. This can be expressed as:
10x + y = 2(x + y) + 8 (Equation 1)
Simplifying Equation 1:
10x + y = 2x + 2y + 8
8x - y = 8 (Equation 1 simplified)
From the second condition, if the digits are interchanged (making the number 10y + x), and divided by the sum of the digits (x+y), the quotient is 8 and the remainder is 2. This can be written as:
10y + x = 8(x + y) + 2 (Equation 2)
Simplifying Equation 2:
10y + x = 8x + 8y + 2
-7x + 2y = 2 (Equation 2 simplified)
Now we have a system of two equations:
1) 8x - y = 8
2) -7x + 2y = 2
Let's solve this system of equations. We can solve for y in equation 1:
y = 8x - 8
Now, substitute this expression for 'y' into equation 2:
-7x + 2(8x - 8) = 2
-7x + 16x - 16 = 2
9x = 18
x = 2
Now, substitute the value of x (x=2) back into the equation y = 8x - 8:
y = 8(2) - 8
y = 16 - 8
y = 8
So, x = 2 and y = 8. Therefore, Mahesh's age is 10x + y = 10(2) + 8 = 28.
Now, let's confirm this using the initial conditions:
* 28 divided by (2+8) = 28/10 = 2 remainder 8. (Correct)
* 82 divided by (8+2) = 82/10 = 8 remainder 2. (Correct)
Therefore, Mahesh's age is 28.