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P started a work by investing Rs.6,000. After 6 months Q jointed with an amount of Rs.14,000. After 1 year R joined with Rs.12,000. After two years of
Question

P started a work by investing Rs.6,000. After 6 months Q jointed with an amount of Rs.14,000. After 1 year R joined with Rs.12,000. After two years of work, they earned a total profit of Rs.45,000. What is the share of P?

A.

Rs.12,000

B.

Rs.12,800

C.

Rs,14,400

D.

Rs,16,000

Correct option is A

Given:
​P  invested Rs.6,000
After 6 months Q invested Rs.14,000
After 1 year R invested Rs.12,000

Formula Used:
Individual Share=Individual InvestmentTotal Investment×Total Profit\text{Individual Share} = \frac{\text{Individual Investment}}{\text{Total Investment}} \times \text{Total Profit}​​

Solution:
​Let's calculate the investment of each person in terms of months:
P: Invested Rs.6000 for 24 months, equivalent to ​6000×24=1440006000 \times 24 = 144000​​
Q: Invested Rs.14000 for 18 months, equivalent to 14000×18=25200014000 \times18 = 252000​​
​​R: Invested Rs.12000 for 12 months, equivalent to 12000×12=14400012000 \times 12 = 144000​​
Total investment in terms of months: 144000+252000+144000=540000144000 + 252000 + 144000 = 540000
For P's share of the profit:

P’s share=(P’s investmentTotal investment)×Total profit\text{P's share} = \left( \frac{\text{P's investment}}{\text{Total investment}} \right) \times \text{Total profit}
​​=(144000540000)×45000=\left( \frac{144000}{540000} \right) \times 45000​​​
=Rs.12,000=Rs. 12,000​​

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