Question:
P and Q start a business with initial investment Rs.5000 and Rs.4000 respectively. After ’t’ years Q adds 25% of what he invested initially and another person R joins the business with them with initial investment Rs.7000 and after 5years from the start of the business P adds Rs.1000 more to his capital. If at the end of 8 years total profit from the business is Rs.11900 while share of Q is Rs.3750, what is the share of R in the profit.
P and Q start a business with initial investment Rs.5000 and Rs.4000 respectively. After ’t’ years Q adds 25% of what he invested initially and another person R joins the business with them with initial investment Rs.7000 and after 5years from the start of the business P adds Rs.1000 more to his capital. If at the end of 8 years total profit from the business is Rs.11900 while share of Q is Rs.3750, what is the share of R in the profit.
Updated On: Jun 30, 2026
- Rs 4250
- Rs 3850
- Rs 4050
- Rs 4850
Show Solution
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The Correct Option is B
Solution and Explanation
The correct option is (B): Rs 3850.
Ratio of their profit = [5000 * 5 + 6000 * 3]: [4000 * t + 5000 * (8 - t)]: [7000 * (8 - t)]
Let total profit = [5000 * 5 + 6000 * 3] + [4000 * t + 5000 * (8 - t)] + [7000 * (8 - t)]=[139000 - 8000t]
Share of Q in the profit = [4000 * t + 5000 * \(\frac{(8 - t)]}{[139000 - 8000t]}\) \(\frac{(8 - t)]}{[139000 - 8000t] }\)= \(\frac{3750}{11900}\)
\(\frac{(160 - 4t)}{(1390 - 80t)}\) = \(\frac{15}{119}\)
119(160 - 4t) = 15(1390 - 80t)
19040 - 476t = 20850 - 1200t
724t = 1810
t = 2.5
Ratio of their profit = [5000 * 5 + 6000 * 3]: [4000 * t + 5000 * (8 - t)]: [7000 * (8 - t)]
= 43000: 37500: 38500 = 86: 75: 77
Share of R in the business = 11900 * (\(\frac{77}{238}\)) = Rs.3850
Ratio of their profit = [5000 * 5 + 6000 * 3]: [4000 * t + 5000 * (8 - t)]: [7000 * (8 - t)]
Let total profit = [5000 * 5 + 6000 * 3] + [4000 * t + 5000 * (8 - t)] + [7000 * (8 - t)]=[139000 - 8000t]
Share of Q in the profit = [4000 * t + 5000 * \(\frac{(8 - t)]}{[139000 - 8000t]}\) \(\frac{(8 - t)]}{[139000 - 8000t] }\)= \(\frac{3750}{11900}\)
\(\frac{(160 - 4t)}{(1390 - 80t)}\) = \(\frac{15}{119}\)
119(160 - 4t) = 15(1390 - 80t)
19040 - 476t = 20850 - 1200t
724t = 1810
t = 2.5
Ratio of their profit = [5000 * 5 + 6000 * 3]: [4000 * t + 5000 * (8 - t)]: [7000 * (8 - t)]
= 43000: 37500: 38500 = 86: 75: 77
Share of R in the business = 11900 * (\(\frac{77}{238}\)) = Rs.3850
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