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)28 : 49 : 64
(c)38 : 28 : 21
(d)None of these
Answer
Answer (as printed): D
Explanation
Let their investments be ₹ $x$ for 14 months; ₹ $y$ for 8 months and ₹ $z$ for 7 months respectively. Then, $14 x: 8 y: 7 z=5: 7: 8$. Now, $\quad \frac{14 x}{8 y}=\frac{5}{7} \Leftrightarrow 70 x=40 y \Leftrightarrow y=\frac{7}{4} x$. And, $\frac{14 x}{7 z}=\frac{5}{8} \Leftrightarrow 112 x=35 z \Leftrightarrow z=\frac{112}{35} x=\frac{16}{5} x$. $\therefore \quad x: y: z=x: \frac{7}{4} x: \frac{16}{5} x=20: 35: 64$.
Explanation as extracted from the printed page; notation may be imperfect.