A sum of money is to be distributed among four members A, B, C, and D in the ratio $ 4 : 7 : 9 : 3 $. If C get

Question

A sum of money is to be distributed among four members A, B, C, and D in the ratio $ 4 : 7 : 9 : 3 $. If C gets $₹720 $ more than D, find D's share.

Examoogle · Accepted Answer

The correct answer is Option A: ₹360. Find the difference in ratio units for C and D (9 - 3 = 6 units), equate to the actual difference (6 units = ₹720), then find 1 unit (120) and multiply by D's ratio (3 × 120 = 360).

Step-by-Step Solution & Concepts:
Shortcut Trick: Find the difference in ratio units for C and D (9 - 3 = 6 units), equate to the actual difference (6 units = ₹720), then find 1 unit (120) and multiply by D's ratio (3 × 120 = 360).

Formula Used: $$C - D = (9x - 3x) = 6x = 720$$

Given: Ratio of shares of A, B, C, and D is 4:7:9:3. The difference between C's share and D's share is ₹720.

Steps: Define the ratio variables: Let the shares of members A, B, C, and D be $4x$, $7x$, $9x$, and $3x$ respectively.. Formulate the equation: Since C gets ₹720 more than D, we calculate the difference between their ratio shares: $9x - 3x = 720$.. Calculate the value of x: Divide the total difference by the number of units: $x = \frac{720}{6} = 120$.. Find D's share: Substitute $x=120$ into D's share expression ($3x$): $3 	imes 120 = 360$.

Answer: A is correct because the difference of $6x$ units equals ₹720, making $x = 120$, so D's share $3x = ₹360$.

Exam Tip: This concept of 'units' in ratios is fundamental to solving problems in Mixtures, Partnerships, and Ages.

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