Discussion
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. Year-wise annual rates of interest offered by these companies are shown by the line graph provided below.
| Year | P | Q |
|---|---|---|
| 2000 | 7 | 6.5 |
| 2001 | 9 | 8 |
| 2002 | 8 | 9.5 |
| 2003 | 10 | 8 |
| 2004 | 7.5 | 9 |
| 2005 | 6.5 | 8 |
| 2006 | 6 | 4 |
If the amounts invested in the companies, P and Q, in 2006 are in the ratio 8:9, then the amounts received after one year as interests from companies P and Q would be in the ratio:
Answer: D
The interest is in the ratio 4:3.
In 2006 the graph gives P's rate as 6% and Q's as 4%. Interest is amount times rate, so with amounts in the ratio 8:9:
\[ \begin{aligned} \frac{I_{P}}{I_{Q}} &= \frac{8 \times 6}{9 \times 4} \\ &= \frac{48}{36} = \frac{4}{3} \end{aligned} \]
P earns more despite the smaller deposit because its rate is one and a half times Q's. The ratios 2:3, 3:4 and 6:7 all put Q ahead, which would need Q's rate to be the higher one, as it was in 2002, 2004 and 2005 but not in 2006.
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