A, B, C enter into a partnership. A contributes \({\displaystyle\frac{2}{5}}^{\text{th}}\) of the capital, while C contributes an amount as much as A and B together contribute. Then the ratio of the capitals is :
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 4 : 1 : 5
Take the total capital as 1. C contributes as much as A and B together, so C is half of the total:
\(A + B + C = 1,\quad C = A + B\)
\(2C = 1\)
\( \displaystyle C = \frac{1}{2} \)
\( \displaystyle B = \frac{1}{2} - \frac{2}{5} = \frac{1}{10} \)
The ratio of the capitals:
\( \displaystyle A : B : C = \frac{2}{5} : \frac{1}{10} : \frac{1}{2} \)
Multiplying each term by 10:
\(A : B : C = 4 : 1 : 5\)