Two finance companies, P and Q, declared fixed annual rates of interest on the amounts invested with them. The rates of interest offered by these companies may differ from year to year. In 2006, company P offered 6% annual interest and company Q offered 4% annual interest.
If the amounts invested in companies P and Q in 2006 are in the ratio 8:9, then the amounts received after one year as interest from companies P and Q would be in the ratio:
Options:
(A) 2:3
(B) 3:4
(C) 6:7
(D) 4:3
Official Answer Key:
D
Step-by-Step Solution & Explanation
• Let the amounts invested in companies P and Q in 2006 be $8k$ and $9k$, respectively.
• Annual interest rate offered by company P in 2006 = $6\%$.
• Annual interest rate offered by company Q in 2006 = $4\%$.
• Interest earned from company P: $I_P = 8k \times \frac{6}{100} = 0.48k$.
• Interest earned from company Q: $I_Q = 9k \times \frac{4}{100} = 0.36k$.
• Ratio of interests:
$\frac{I_P}{I_Q} = \frac{0.48k}{0.36k} = \frac{48}{36} = \frac{4}{3}$
• Final Answer: (D) 4:3
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