A, B, C enter into a partnership. A contributes $\frac{2^{th}}{5}$ of the capital, while C contributes an amount as much as A and B together contribute. Then the ratio of the capitals is :

4 : 1 : 5

The correct answer is Option (3) → 4 : 1 : 5

Let the total contribution be T

A's contribution = $\frac{2}{5}T$

Let B's contribution be B.

∴ C's contribution = $\frac{2}{5}T+B$

$⇒T=\frac{2}{5}T+B+\left(\frac{2}{5}T+B\right)$

$⇒T=\frac{4}{5}T+2B$

$⇒B=\frac{1}{10}T$

$∴A:B:C=\frac{2}{5}T:\frac{1}{10}T:\frac{1}{2}T$

$=4 : 1 : 5$