Sum now and ratio 10 years ago: The sum of the present ages of Yogesh, Prakash, and Sameer is 93. Ten years ago their ages were in the ratio 2 : 3 : 4. What is Sameer’s present age?

Introduction / Context:Translate a past ratio into algebraic ages then, and shift forward by 10 years to reach present ages. Sum must match 93; solve for the scale factor and extract Sameer’s present age.

Given Data / Assumptions:

• Present sum = 93
• 10 years ago ratio = 2 : 3 : 4

Concept / Approach:Let past ages be 2x, 3x, 4x. Present ages are 2x+10, 3x+10, 4x+10. Sum equals 93; solve for x and then compute Sameer = 4x + 10.

Step-by-Step Solution:

Verification / Alternative check:Present ages sum to 93: (24 + 10) + (21 + 10) + (28 + 10) = 93 ✓.

Why Other Options Are Wrong:32, 24, 34 do not match the computed 38; hence “None of these.”

Common Pitfalls:Adding 10 only once to the total; each person’s age increases by 10.

Final Answer:None of these (Sameer’s present age is 38 years).