A, B and C entered into a partnership with capitals of Rs 60,000, Rs 50,000 and Rs 70,000 respectively. C joined \(x\) months after the start of the year and A left \(y\) months before the end of the year. At the end of the year they shared the profit in the ratio A : B : C = 18 : 20 : 21. Find \(x\) and \(y\).
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \(x=3,\ y=3\)
Profit is shared in the ratio of capital × months. B stayed for all 12 months, so his product fixes the value of one part of the ratio.
B: \(50000\times12=600000\), which is 20 parts, so 1 part \(=30000\)
A: \(60000\times(12-y)=18\times30000=540000\), so \(12-y=9\) and \(y=3\)
C: \(70000\times(12-x)=21\times30000=630000\), so \(12-x=9\) and \(x=3\)
So \(x=3\) and \(y=3\): C joined after 3 months and A left 3 months before the end.
Why the other options are incorrect
Option (1) \(x=9,\ y=9\) — Incorrect. 9 is the number of months A and C stayed, not the months they were away.
Option (3) \(x=3,\ y=9\) — Incorrect. With \(y=9\), A stays only 3 months and gets \(60000\times3=180000\), just 6 parts, not 18.
Option (4) \(x=9,\ y=3\) — Incorrect. With \(x=9\), C stays only 3 months and gets \(70000\times3=210000\), just 7 parts, not 21.