GATE Civil 2016 Set 2 | GA | Question: 6

Question

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 offered by these companies are shown by the line graph provided below.

 

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:

• A. $2:3$
• B. $3:4$
• C. $6:7$
• D. $4:3$

Comments

Let investment in company p is 8x and investment in company q is 9x .
Amount of interest received from company p is 6%8x=.48x
Similarly interesr received from company q is 4 percent of 9x=.36x
Ratio is 4/3

Answer 1

The amounts invested in the companies, $P$ and $Q$, in $2006$ are in the ratio $8:9$

The annual rate of interest in the companies $P$ and $Q$ are $6\%$ and $4\%$ respectively in the year $2006$

∴ The amounts received after one year as interests from companies $P$ and $Q$ would be in the ratio

$\left(8\times \dfrac{6}{100}\right) : \left(9\times \dfrac{4}{100}\right)$

$= 48:36$

$={4:3}$

Answer 2

Since t=1year, SI = CI.

For P :
           (8x * 6 * 1)/100

For Q :
          (9x * 4 * 1)/100

P:Q = 4:3

Answer : (d)

Answer 3

The interest earned on an investment over a fixed time period depends on two factors:

1. Principal Amount ($P$): The total sum of money invested.

2. Annual Interest Rate ($R$): The percentage yield provided by the financial institution per year.

Simple Interest formula is:

$$\text{Interest} = \frac{P \times R \times T}{100}$$

For a time period of $T = 1\text{ year}$:

$$\text{Interest} = \frac{P \times R}{100}$$

Ratio of interest earned from Company $P$ ($\text{I}_P$) to Company $Q$ ($\text{I}_Q$):

$$\frac{\text{I}_P}{\text{I}_Q} = \frac{\left(\frac{P_P \times R_P}{100}\right)}{\left(\frac{P_Q \times R_Q}{100}\right)} = \frac{P_P \times R_P}{P_Q \times R_Q} = \left(\frac{P_P}{P_Q}\right) \times \left(\frac{R_P}{R_Q}\right)$$