₹6,083 is divided among A, B, C and D in such a way that the shares of A and…
2025
₹6,083 is divided among A, B, C and D in such a way that the shares of A and B, B and C and C and D are in the ratios of 2 : 3, 4 : 5 and 10 : 3, respectively. The share of A (in ₹) is:
Answer: B. 1,232 — When three ratios link four quantities in a chain — A:B, B:C and C:D — they can be combined into one continued ratio A:B:C:D by scaling each ratio so that the…
- A.
1,142
- B.
1,232
- C.
1,302
- D.
1,352
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Correct answer: B
When three ratios link four quantities in a chain — A:B, B:C and C:D — they can be combined into one continued ratio A:B:C:D by scaling each ratio so that the term it shares with its neighbour (first B, then C) reads the same value in both; the amount to be divided is then split into parts proportional to that combined ratio, where one part equals the total divided by the sum of the ratio terms.
Applying this to the given data:
A:B = 2:3 and B:C = 4:5. Scale A:B by 4 and B:C by 3 so B reads 12 in both: A:B = 8:12 and B:C = 12:15, giving A:B:C = 8:12:15.
C:D = 10:3. Scale it by 1.5 so C reads 15 (its value in A:B:C): C:D = 15:4.5. Doubling every term clears the fraction, giving the whole-number combined ratio A:B:C:D = 16:24:30:9.
The ratio terms add to 16 + 24 + 30 + 9 = 79, so one part equals ₹6,083 ÷ 79 = ₹77.
The share of A is 16 parts, so A = 16 × ₹77 = ₹1,232.
Checking: B = 24 × 77 = ₹1,848, C = 30 × 77 = ₹2,310 and D = 9 × 77 = ₹693; the four shares add to 1,232 + 1,848 + 2,310 + 693 = ₹6,083, and A:B = 1,232:1,848 = 2:3, B:C = 1,848:2,310 = 4:5, C:D = 2,310:693 = 10:3 — all three given ratios hold.
So the share of A is ₹1,232.