Proportional distribution among sons, daughters, and friends ₹ 17200 is divided among 5 sons, 4 daughters, and 2 friends. Each daughter gets 4 times each friend, and each son gets 5 times each friend. How much does each daughter receive?

Introduction / Context:
Weighted distribution problems assign different multiples of a base share to different groups. By expressing all shares in terms of a single unit (the friend’s share), the total amount can be partitioned precisely.

Given Data / Assumptions:

• Total amount = ₹ 17200.
• 5 sons, 4 daughters, 2 friends.
• Each daughter gets 4 times each friend; each son gets 5 times each friend.
• Let x = amount received by each friend.

Concept / Approach:
Convert all recipients’ amounts into multiples of x. Sum all “x” units across recipients to get the total in terms of x, then solve for x. Multiply x by 4 to find each daughter’s amount.

Step-by-Step Solution:
Friend’s share = x ⇒ total for 2 friends = 2x.Each daughter = 4x ⇒ total for 4 daughters = 16x.Each son = 5x ⇒ total for 5 sons = 25x.Grand total = 2x + 16x + 25x = 43x.43x = 17200 ⇒ x = 17200 / 43 = 400.Each daughter receives 4x = 4 * 400 = ₹ 1600.

Verification / Alternative check:
Compute all: sons = 25*400 = 10000; daughters = 16*400 = 6400; friends = 2*400 = 800; total = 10000 + 6400 + 800 = 17200. Perfect match.

Why Other Options Are Wrong:
₹ 800, ₹ 1000, ₹ 1500 are not equal to 4x when x = 400; they either reflect the friend’s share or incorrect multiples.

Common Pitfalls:
Forgetting to multiply by the count of people in each category; mixing up the multiples (4x vs 5x). Always total the weighted counts first, then back-solve for x.

Final Answer:
₹ 1600