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

To solve the problem, we will use the concept of simple interest. Simple interest is calculated using the formula:

\(I = \frac{P \times R \times T}{100}\) 

Where \(I\) is the interest, \(P\) is the principal amount, \(R\) is the rate of interest per annum, and \(T\) is the time in years.

Let's analyze the information given:

• The principal amount is denoted by Rs. XYZ.
• The time period is 3 years.
• If the rate of interest is increased by 2%, the extra interest earned is Rs. 360.

We need to find the value of the principal amount, Rs. XYZ. Let us denote the initial rate of interest as \(R\%\).

According to the problem, the extra interest earned at a rate 2% higher is Rs. 360. Hence:

\(I_{extra} = \frac{P \times (R+2) \times 3}{100} - \frac{P \times R \times 3}{100} = 360\)

Simplifying, we have:

\(\frac{P \times (R+2) \times 3}{100} - \frac{P \times R \times 3}{100} = \frac{P \times 2 \times 3}{100} = 360\)

This simplifies to:

\(\frac{P \times 6}{100} = 360\)

Now, solving for \(P\) (Rs. XYZ), we multiply both sides by 100 and divide by 6:

\(P = \frac{360 \times 100}{6} = 6000\)

Therefore, the principal amount, Rs. XYZ, is Rs. 6000. Thus, the correct answer is:

• Rs. 6000

Answer 2

Step 1: Set up the simple interest formula for both rates.
Let the principal be P and the original rate be x% per year. Simple interest for 3 years at the original rate is \(SI_1 = \frac{P \times 3 \times x}{100}\). At a rate 2% higher, it is \(SI_2 = \frac{P \times 3 \times (x+2)}{100}\).

Step 2: Find the difference between the two interests.
\(SI_2 - SI_1 = \frac{P \times 3 \times (x+2)}{100} - \frac{P \times 3 \times x}{100} = \frac{P \times 3 \times 2}{100} = \frac{6P}{100}\). Notice x cancels out completely, so the original rate is never actually needed.

Step 3: Use the given difference to solve for P.
We are told this difference is Rs. 360, so \(\frac{6P}{100} = 360\).

Step 4: Solve the equation.
Multiply both sides by 100: \(6P = 36000\). Divide by 6: \(P = 6000\).

Final Answer:
The deposited amount, Rs. XYZ, is Rs. 6000. \[ \boxed{Rs.\ 6000} \]