Question

In 4 years, Rs. 6000 amounts to Rs. 8000. In what time at the same rate will Rs. 525 amount to Rs. 700?

• A. 2 years
• B. 3 years
• C. 4 years
• D. 5 years

Hint:

Find the rate from the first case using SI = PRT/100, then apply the same rate to the second case and solve for time.

Answer 1

The Correct Option is C

Skip finding the rate directly, and instead compare the two cases using ratios, since both run at the same rate of interest.

In the first case, principal Rs. 6000 earns Rs. 2000 interest in 4 years. That means Rs. 6000 earns Rs. 500 interest per year, so the annual interest works out to $\frac{500}{6000}$ of the principal each year.

In the second case, the principal is Rs. 525, and the needed interest is Rs. 175. Per year, at the same rate, Rs. 525 would earn $525 \times \frac{500}{6000} = Rs.\ 43.75$ interest.

Now find how many such years are needed to reach Rs. 175 of interest: $\frac{175}{43.75} = 4$ years.

Let's summarize:

• First case gives an annual interest worth Rs. 500 per Rs. 6000, i.e. $25/3\%$.
• Applying it to Rs. 525 gives Rs. 43.75 interest per year.
• Rs. 175 needed interest divided by Rs. 43.75 per year gives exactly 4 years.

This matches option C without solving explicitly for the percentage rate first.