### 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?

A. 5 : 7 : 8 B. 20 : 49 : 64 C. 38 : 28 : 21 D. None of these Answer: Option B

### Solution(By Apex Team)

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{14x}{8y}=\frac{5}{7}\Rightarrow98x=40y\\ &\Rightarrow y=\frac{49x}{20}\\ &\text{ And, }\frac{14x}{7z}=\frac{5}{8}\\ &\Rightarrow112x=35z\\ &\Rightarrow z=\frac{112x}{35}=\frac{16x}{5}\\ &\text{ So }x:y:z=x:\frac{49x}{20}:\frac{16x}{5}\\ &\text{ (Multiply by 20) }\\ &\Rightarrow20:49:64\end{aligned}

A. 5 : 7 : 8
B. 20 : 49 : 64
C. 38 : 28 : 21
D. None of these

A. Rs. 4000
B. Rs. 5000
C. Rs. 6000
D. Rs. 7000

A. Rs. 2380
B. Rs. 2300
C. Rs. 2280
D. Rs. 2260