The amount Rs 2,100 became Rs 2,352 in 2 years at simple interest. If the interest rate is decreased by 1 % what is the new interest ?

Options

A. Rs 210
B. Rs 220
C. Rs 242
D. Rs 252

Answer

To solve the problem step by step, we will follow the simple interest formula and calculate the new interest after decreasing the interest rate by 1%.

### Step 1: Identify the given values
- Principal (P) = Rs 2,100
- Amount (A) = Rs 2,352
- Time (T) = 2 years

### Step 2: Calculate the Simple Interest (SI)
The formula for calculating Simple Interest is:
\[ \text{SI} = A - P \]

Substituting the values:
\[ \text{SI} = 2,352 - 2,100 \]
\[ \text{SI} = 252 \]

### Step 3: Calculate the Rate of Interest (R)
Using the formula for Simple Interest:
\[ \text{SI} = \frac{P \times R \times T}{100} \]

We can rearrange this to find R:
\[ R = \frac{\text{SI} \times 100}{P \times T} \]

Substituting the known values:
\[ R = \frac{252 \times 100}{2,100 \times 2} \]
\[ R = \frac{25200}{4200} \]
\[ R = 6\% \]

### Step 4: Decrease the Rate of Interest by 1%
New Rate (R2):
\[ R2 = R - 1\% = 6\% - 1\% = 5\% \]

### Step 5: Calculate the New Simple Interest (SI2)
Using the new rate:
\[ \text{SI2} = \frac{P \times R2 \times T}{100} \]

Substituting the values:
\[ \text{SI2} = \frac{2,100 \times 5 \times 2}{100} \]
\[ \text{SI2} = \frac{21,000}{100} \]
\[ \text{SI2} = 210 \]

### Final Answer
The new interest after decreasing the interest rate by 1% is Rs 210.

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