Recover ages from past ratio and present sum: The present total of ages of A, B, and C is 90. Ten years ago their ratio was 1 : 2 : 3. What is B’s present age?

Introduction / Context:Backdating ratios is common in age problems. Convert the past ratio into algebraic ages “then,” add the elapsed time to each, and match the present total to find the scale factor.

Given Data / Assumptions:

• Present sum = 90
• 10 years ago ratio = 1 : 2 : 3

Concept / Approach:Let ages 10 years ago be x, 2x, 3x. Present ages are x+10, 2x+10, 3x+10. Sum them to 90 and solve for x, then compute B = 2x + 10.

Step-by-Step Solution:

Verification / Alternative check:Present ages are 20, 30, 40 which indeed sum to 90; roll back 10 years gives 10, 20, 30 = 1 : 2 : 3.

Why Other Options Are Wrong:20 and 40 mismatch the computed 30; “None of these” is unnecessary.

Common Pitfalls:Applying the 10-year shift to the sum only; each person’s age must be adjusted individually before summing.

Final Answer:30 years