Five years ago, Sushma was 5 times as old as her son. Five years from now, Sushma's age will be 8 years less than three times her son's age at that time. What are the present ages of Sushma and her son (in years)?

Introduction:
This is a classic ages equation problem involving “years ago” and “years hence” with multiplicative relations. The key is to define variables for present ages, then carefully shift them backward or forward in time based on the statement. Once both conditions are converted into equations, solve them like a simple linear system to get present ages.

Given Data / Assumptions:

• Let Sushma's present age = M years
• Let son's present age = S years
• 5 years ago: M - 5 = 5 * (S - 5)
• 5 years hence: M + 5 = 3 * (S + 5) - 8

Concept / Approach:
Convert time-shift statements into equations. Solve the two equations to find S and M. Ensure ages remain positive and logically consistent.

Step-by-Step Solution:
From 5 years ago: M - 5 = 5(S - 5)M - 5 = 5S - 25M = 5S - 20From 5 years hence: M + 5 = 3(S + 5) - 8M + 5 = 3S + 15 - 8 = 3S + 7M = 3S + 2Equate: 5S - 20 = 3S + 22S = 22 => S = 11M = 3*11 + 2 = 35

Verification / Alternative check:
5 years ago: M-5 = 30 and S-5 = 6, and 5*6 = 30, correct. 5 years hence: M+5 = 40 and S+5 = 16, 3*16 - 8 = 48 - 8 = 40, correct.

Why Other Options Are Wrong:
33 and 15: fails the “5 times” condition 5 years ago.48 and 24: gives huge ages and does not satisfy the -8 adjustment.24 and 13: makes mother too young to have a son of 13.40 and 12: does not satisfy both equations simultaneously.

Common Pitfalls:
Applying the multiplier to the present age instead of the age 5 years ago.Forgetting that “8 less than” means subtract 8 after multiplying.Mixing up “years hence” and “years ago” signs.

Final Answer:
35 years and 11 years