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

Answer 1

The Correct Option is C

To solve this problem, we use the formula for simple interest: \(SI = \frac{P \times R \times T}{100}\) where \(SI\) is the simple interest, \(P\) is the principal amount, \(R\) is the rate of interest per annum, and \(T\) is the time in years.

Let \(P = \text{Rs. XYZ}\) and the initial rate be \(R\%\). The simple interest at this rate for 3 years is \(\frac{P \times R \times 3}{100}\).

If the rate is increased by 2%, the new rate is \((R + 2)\%\) and the simple interest becomes \(\frac{P \times (R + 2) \times 3}{100}\).

According to the problem, the increase in interest is Rs. 360 more. Thus,

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

Simplifying, we get:

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

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

Multiplying both sides by 100,

\(P \times 6 = 36000\)

Dividing both sides by 6,

\(P = 6000\)

Therefore, the principal amount Rs. XYZ is Rs. 6000.

Options
Rs. 5500
Rs. 5000
Rs. 6000
Rs. 4500