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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 the difference between C's and B's shares.
₹240
₹480
₹160
₹360
₹240
Find the unit value 'k' by subtracting the ratios of C and D (9−3=6), so 6k=720⇒k=120. The requested difference between C and B is (9−7)k=2k=2(120)=240.
Ratio of shares A:B:C:D = 4:7:9:3. C gets ₹720 more than D.
Value=Ratio share×k
Find the unit value 'k' by subtracting the ratios of C and D (9−3=6), so 6k=720⇒k=120. The requested difference between C and B is (9−7)k=2k=2(120)=240.
Students often calculate the total sum instead of finding the requested difference between specific members (C and B).
Define the ratio variables
Let the shares of A, B, C, and D be 4k, 7k, 9k, and 3k respectively.
A=4k,B=7k,C=9k,D=3k
Calculate the constant k
Given that C gets ₹720 more than D, we set up the equation C−D=720. Substituting the ratio values gives 9k−3k=720.
6k=720⟹k=120
Find the difference between C and B
The difference between C's share (9k) and B's share (7k) is 9k−7k=2k. Substituting k=120 gives 2×120=240.
2k=2×120=240
A is correct because the calculated difference between C and B's shares is ₹240.
Always identify the difference in ratio units first before multiplying by the constant value to save time in competitive exams.
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