Question

Rs. XYZ was deposited at simple interest at a specific rate for 3 years. Had it been deposited at 2% higher rate, it would have fetched Rs. 360 more. Find Rs. XYZ.

• A. Rs. 5500
• B. Rs. 5000
• C. Rs. 6000
• D. Rs. 4500

Hint:

The original rate cancels out; only the 2% rate increase over 3 years matters for the Rs. 360 difference.

Answer 1

The Correct Option is C

Step 1: Recall a shortcut for this kind of problem.
Extra simple interest earned only depends on the principal, the time, and how much the rate increased, since the original rate cancels out. The shortcut is: Extra Interest $= \frac{P \times \text{Time} \times \text{Rate increase}}{100}$.

Step 2: Plug in the known numbers.
Time = 3 years, Rate increase = 2%, Extra Interest = Rs. 360. So $360 = \frac{P \times 3 \times 2}{100} = \frac{6P}{100}$.

Step 3: Solve for P.
$6P = 360 \times 100 = 36000$, so $P = \frac{36000}{6} = 6000$.

Step 4: Check with a sample rate.
Try an original rate of 5%: interest at 5% for 3 years on Rs. 6000 is $\frac{6000 \times 3 \times 5}{100} = 900$. At 7% (2% higher), interest is $\frac{6000 \times 3 \times 7}{100} = 1260$. The difference is $1260 - 900 = 360$, which matches, confirming P = 6000 regardless of the original rate.

Final Answer:
Rs. XYZ equals Rs. 6000. \[ \boxed{Rs.\ 6000} \]