A sum of ₹53 is divided among A, B and C in such a way that A gets ₹7 more…
2022
A sum of ₹53 is divided among A, B and C in such a way that A gets ₹7 more than what B gets and B gets ₹8 more than what C gets. The ratio of their shares is:
Answer: C. 25:18:10 — CONCEPTWhen three shares differ by fixed amounts, take the smallest share as a variable. Express the other shares using the stated differences, then use the…
- A.
27:20:12
- B.
27:17:09
- C.
25:18:10
- D.
23:19:11
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Correct answer: C
CONCEPT
When three shares differ by fixed amounts, take the smallest share as a variable. Express the other shares using the stated differences, then use the total to form one linear equation.
APPLICATION
Let C’s share be ₹x.
Since B gets ₹8 more than C, B’s share is ₹(x + 8).
Since A gets ₹7 more than B, A’s share is ₹(x + 15).
Their total is x + (x + 8) + (x + 15) = 53.
Thus 3x + 23 = 53, so 3x = 30 and x = 10.
Therefore A = ₹25, B = ₹18, and C = ₹10, giving A:B:C = 25:18:10.
CROSS-CHECK
The shares add to 25 + 18 + 10 = 53; also, 25 − 18 = 7 and 18 − 10 = 8. Hence the required ratio is 25:18:10.