Divide a sum by parts given one share: A sum is divided among three persons in the ratio 3 : 4 : 7. If the second person receives ₹ 12, what is the total sum?

Introduction / Context:
When a total is split in a given ratio and one share is known, convert that share into its “number of parts” to find the value per part, and then multiply by the sum of parts to get the total amount.

Given Data / Assumptions:

• Ratio = 3 : 4 : 7.
• Second share (4 parts) = ₹ 12.
• Total parts = 3 + 4 + 7 = 14.

Concept / Approach:
Value per part = Given share / Number of parts for that person. Then Total = (Value per part) * (Total parts).

Step-by-Step Solution:
Value per part = 12 / 4 = ₹ 3.Total = 14 * 3 = ₹ 42.

Verification / Alternative check:
Compute all shares: 3 parts = ₹ 9, 4 parts = ₹ 12, 7 parts = ₹ 21; sum = ₹ 42, consistent.

Why Other Options Are Wrong:

• ₹ 21 and ₹ 9 are partial shares, not the total.
• ₹ 32 does not match the ratio arithmetic.

Common Pitfalls:

• Mistaking the given ₹ 12 as the total instead of just the second person’s share.

Final Answer:
₹ 42