NIMCET 2023 — Reasoning PYQ

Step 1: Understand the Problem
A man invested a certain sum of money at a certain rate of simple interest (SI) and received 60% more after 8 years. We need to find out how much interest he would earn if he invests Rs. 9600 at the same rate for 4 years.
Step 2: Determine the Interest Rate
Since the man received 60% more after 8 years, this 60% represents the total interest earned over that period.
Let the principal amount be P. The total amount after 8 years is:
$$A=P+SI$$
Given that SI is 60% of P:
$$<br>SI=0.6P$$
Thus, the total amount A after 8 years can be expressed as:
$$A=P+0.6P=1.6P$$
Step 3: Calculate the Interest for 4 Years
The interest earned in 8 years is 60%, which means the interest earned in 4 years would be half of that:
Interest for 4 years = $\frac{60\%}{2}=30\%$
Step 4: Calculate the Simple Interest on Rs. 9600
Now, we will calculate the simple interest on Rs. 9600 for 4 years at the rate of 30%.
Using the formula for simple interest:
$$<br>SI=\frac{P\times R\times T}{100}$$
Where:
- $P=9600$
- $R=30$ (the rate of interest)
- $T=4$ (the time period in years)
Substituting the values:
$$SI=\frac{9600\times 30\times 4}{100}$$
Step 5: Simplify the Calculation
Calculating the above expression:
$$<br>SI=\frac{9600\times 120}{100}=\frac{1152000}{100}=11520$$
Step 6: Final Calculation
Thus, the total interest earned after 4 years on Rs. 9600 at 30% simple interest is:
$$SI=2880$$

Conclusion
The total interest he would get after four years is Rs. 2880.