Three partners shared the profit in a business in the ratio 5 : 7 : 8. They had partnered for 14 months, 8 months and 7 months respectively. What was the ratio of their investments?

15 : 7 : 8
220 : 49 : 64
338 : 28 : 21
4None of these

Answer:- 1

Explanation:-

Solution:

Let their investments be Rs. x for 14 months, Rs. y for 8 months and Rs. z for 7 months respectively.
Then, 14x : 8y : 7z = 5 : 7 : 8.
Now,

\begin{aligned} \frac{14 x}{8 y} = \frac{5}{7} \Rightarrow 98 x = 40 y \\ \Rightarrow y = \frac{49 x}{20} \\ And, \frac{14 x}{7 z} = \frac{5}{8} \\ \Rightarrow 112 x = 35 z \\ \Rightarrow z = \frac{112 x}{35} = \frac{16 x}{5} \\ So x : y : z = x : \frac{49 x}{20} : \frac{16 x}{5} \\ (Multiply by 20) \\ \Rightarrow 20 : 49 : 64 \end{aligned}

$\eqalign{ & \frac{{14x}}{{8y}} = \frac{5}{7} \Rightarrow 98x = 40y \cr & \Rightarrow y = \frac{{49x}}{{20}} \cr & {\text{And, }}\frac{{14x}}{{7z}} = \frac{5}{8} \cr & \Rightarrow 112x = 35z \cr & \Rightarrow z = \frac{{112x}}{{35}} = \frac{{16x}}{5} \cr & {\text{So}}\,x:y:z = x:\frac{{49x}}{{20}}:\frac{{16x}}{5} \cr & ({\text{Multiply by 20}}) \cr & \Rightarrow 20:49:64 \cr}$