Question

$D$ started a business $E$ and $F$ together joined the business after few months. If the ratio of their profits is $9: 8: 10$ and the ratio of their investments is $3: 4: 5$, then find after how many months did $E$ and $F$ together joined the business.

• A. 8 months
• B. 4 months
• C. 7 months
• D. 2 months

Answer 1

Answer: (B)

Let $E$ and $F$ are joined in the business after ' $x$ ' months. Ratio of profits $=$ Ratios of products of investments and time periods
$9: 8: 10=3 \times 12: 4 \times(12-x): 5 \times(12-x) $
$\frac{9}{8}=\frac{36}{4(12-x)} $
$9 \times 4(12-x)=8 \times 36 $
$12-x=8 \Rightarrow x=4$
$\therefore E$ and $F$ have joined after 4 months.