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$A, B$ and $C$ 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 be $Rs . 27000 C' s$ share is

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Detailed Solution

Given that

A

invests some money at the beginning,

B

invests double the amount after

6

months and

C

invests thrice the amount after

8

months.
The annual profit is Rs.27000.
Let

A

invested

Rs . x

for

12

months.
Then, according to the question,

B

invested

Rs . 2 x

for

6

months and

C

invested

Rs . 3 x

for

4

months.
Then ratio of their capital is,
Raio

= 12 \times x : 2 x \times 6 : 3 x \times 4

\Rightarrow

Ratio

= 12 x : 12 x : 12 x

\Rightarrow

Ratio

= 1 : 1 : 1

So,

C' s

share of profit will be,
C’s share

= \frac{1}{1 + 1 + 1} \times 27000

\Rightarrow C' s share = \frac{1}{3} \times 27000

\Rightarrow C' s share = Rs . 9000

Thus, C’s share of the profit is Rs.9000.
Therefore, the correct option is 2.

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A,Band C enter into partnership. A invests some money at the beginning, B invests double the amount after 6months and C invests thrice the amount after 8 months. If the annual profit be Rs.27000 C's share is

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$A, B$ and $C$ 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 be $Rs . 27000 C' s$ share is