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 A's share.

Examoogle · Accepted Answer

The correct answer is Option B: ₹480. Calculate the difference between C and D's ratio units (9 - 3 = 6 units). Equate 6 units = 720. So 1 unit = 120. A's share is 4 units = 4 * 120 = 480.

Step-by-Step Solution & Concepts:
Shortcut Trick: Calculate the difference between C and D's ratio units (9 - 3 = 6 units). Equate 6 units = 720. So 1 unit = 120. A's share is 4 units = 4 * 120 = 480.

Formula Used: $$x = \frac{	ext{Difference in values}}{	ext{Difference in ratios}}$$

Given: Ratio of shares of A, B, C, and D is 4:7:9:3. C gets ₹720 more than D.

Steps: Define the ratio variables: Let the common multiplier for the ratio 4:7:9:3 be $x$. Thus, the shares are: A = $4x$, B = $7x$, C = $9x$, and D = $3x$.. Set up the equation based on given data: The problem states C gets ₹720 more than D. This can be expressed as $C - D = 720$.. Solve for x: Simplify the expression: $6x = 720$. Therefore, $x = \frac{720}{6} = 120$.. Calculate A's share: Since A's share is $4x$, substitute $x = 120$ into the expression: $A = 4 	imes 120 = 480$.

Answer: B is correct because the share of A is calculated to be ₹480 based on the ratio multiplier of 120.

Exam Tip: This ratio-based logic is frequently used in Partnership, Profit & Loss, and Age problems in competitive exams.

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