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$A$ and $B$ started a partnership business investing some amount in the ratio of $3 : 5$ , C joined them after six months with an amount equal to that of $B .$ In what proportion should the profit at the end of one year be distributed among $A, B$ and $C$ ?

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3 : 5 : 2

3 : 5 : 5

6 : 10 : 5

None

answer is C.

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Detailed Solution

Given,
Ratio of the amount invested by A and B = 3: 5
Amount of C= Amount of B
Time at which C joined = 6 months later
Let the initial investments of

A

and

B

3 x

and

5 x

. So the investment of

C

is also

5 x .

So, the ratio of profits distributed among them is given by,

A : B : C = (3 x \times 12) : (5 x \times 12) : (5 x \times 6)

\Rightarrow A : B : C = 36 : 60 : 30

\Rightarrow A : B : C = 6 : 10 : 5

Thus, the ratio of the profits is

6 : 10 : 5

.
Therefore, the correct option is 3.

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