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A, B, C enter into partnership. A invests some money at the beginning, B invests double the amount after $6$ months and C invests thrice the amount after $8$ months. If the annual profit is Rs $27, 000$ then find C's share.

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Rs . 11, 250

Rs . 9, 000

Rs.

10, 800

Rs . 8, 625

answer is B.

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Detailed Solution

It is given that A, B and C are in partnership. B invests double the amount of A after 6 months and C invests thrice of A after 8 months. And annual profit is Rs. 27000.
Let the amount A invest is Rs

x

.
Time period of investment of A is

12

months.
Amount B invest is Rs

2

x.
Time period of investment of B is

6

months.
Amount C investment is Rs

3

x.
Time period of investment of C is

4

months.
Profit is divided in the ratio = Amount of investment

\times

Time period of investment

P_{A} : P_{B} : P_{C} = (x \times 12) : (2 x \times 6) : (3 x \times 4)

\Rightarrow P_{A} : P_{B} : P_{C}

12 x : 12 x : 12 x

So,

P_{A} {: P}_{B} {: P}_{C} = 1 : 1 : 1

.
C's share of profit =

\frac{1}{3} \times 27000

\Rightarrow

C's share of profit

= Rs . 9000

So, C’s share is Rs. 9000.
Hence, the correct option is 2.

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