P, Q and R enter into a partnership. P advances one-fourth of the capital for one-fourth of the time. Q contributes one-fifth of the capital for half of the time. R contributes the remaining capital for the whole time. How should they divide a profit of Rs 1140?
Solution
Correct Answer: Option D
We know that, required profits would be in the ratio:
⇒ P’s share × P’s time : Q’s share × Q’s time : R’s share × R’s time
\(= \frac{1}{4} \times \frac{1}{4}\;:\frac{1}{5} \times \frac{1}{2}\;:\left\{ {1 - \left( {\frac{1}{4} + \frac{1}{5}} \right)} \right\} \times 1\)
\(= \frac{1}{{16}}\;:\frac{1}{{10}}\;:\frac{{11}}{{20}}\)
= 5 : 8 : 44
Now,
⇒ P’s share in profit \(= \frac{5}{{57}} \times 1140 = Rs.100\)
⇒ Q’s share in profit \(= \frac{8}{{57}} \times 1140 = Rs.160\)
⇒ R’s share in profit \(= \frac{{44}}{{57}} \times 1140 = Rs.880\)
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