Question
A, B and C entered into a partnership. A invested Rs. 2560 and B invested Rs. 2000. At the end of the year, they gained Rs. 1105, out of which A got Rs. 320. C's capital was ?
Answer: Option C
Let C's capital be Rs. x
Then,
A : B : C = 2560 : 2000 : x
$$\eqalign{
& {\text{A's share}} \cr
& = {\text{Rs}}{\text{.}}\left( {1105 \times \frac{{2560}}{{4560 + x}}} \right) \cr
& \therefore 1105 \times \frac{{2560}}{{4560 + x}} = 320 \cr
& \Rightarrow 320x + 1459200 = 2828800 \cr
& \Rightarrow 320x = 1369600 \cr
& \Rightarrow x = 4280 \cr} $$
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Let C's capital be Rs. x
Then,
A : B : C = 2560 : 2000 : x
$$\eqalign{
& {\text{A's share}} \cr
& = {\text{Rs}}{\text{.}}\left( {1105 \times \frac{{2560}}{{4560 + x}}} \right) \cr
& \therefore 1105 \times \frac{{2560}}{{4560 + x}} = 320 \cr
& \Rightarrow 320x + 1459200 = 2828800 \cr
& \Rightarrow 320x = 1369600 \cr
& \Rightarrow x = 4280 \cr} $$
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