Discussion
X and Y shared profit in the ratio of 7 : 3. Z was admitted as a partner. X surrendered 1/7 of his share and Y 1/3 of his share in favour of Z. The new ratio will be ................
Answer: A
The new ratio is 3 : 1 : 1.
\[ \begin{aligned} \text{X gives} &= \tfrac{7}{10} \times \tfrac{1}{7} = \tfrac{1}{10} \\ \text{Y gives} &= \tfrac{3}{10} \times \tfrac{1}{3} = \tfrac{1}{10} \end{aligned} \]
\[ \begin{aligned} \text{X} &= \tfrac{7}{10} - \tfrac{1}{10} = \tfrac{6}{10} \\ \text{Y} &= \tfrac{3}{10} - \tfrac{1}{10} = \tfrac{2}{10} \\ \text{Z} &= \tfrac{1}{10} + \tfrac{1}{10} = \tfrac{2}{10} \end{aligned} \]
So the ratio is 6 : 2 : 2, which simplifies to 3 : 1 : 1. The other ratios come from treating the fractions as fractions of the whole profit rather than of each partner's own share.
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