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.

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

Tardigrade Admin · Accepted Answer

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 × 12: 4 ×(12-x): 5 ×(12-x) (9/8)=(36/4(12-x)) 9 × 4(12-x)=8 × 36 12-x=8 ⇒ x=4 ∴ E and F have joined after 4 months.

Q. 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.

8 months

4 months

7 months

2 months

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=3×12:4×(12−x):5×(12−x) 89​=4(12−x)36​ 9×4(12−x)=8×36 12−x=8⇒x=4 ∴E and F have joined after 4 months.

Q. $D$ 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.