💰 Question 59: Simple Interest Problem

Q59: In how many years does a sum of ₹1200 become ₹1800 at a simple interest rate of 5% per annum?

Options:
(a) 10 years
(b) 20 years
(c) 15 years

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📝 Step 1: Recall the simple interest formula

$$\text{Simple Interest (SI)} = \frac{\text{Principal (P)} \times \text{Rate (R)} \times \text{Time (T)}}{100}$$

We are given:

• Principal $P = 1200$

• Final Amount $A = 1800$

• Rate $R = 5\%$ per annum

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📝 Step 2: Find the simple interest

$$\text{SI} = \text{Amount} - \text{Principal} = 1800 - 1200 = 600$$

✅ So, the interest earned = ₹600

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📝 Step 3: Use SI formula to find time

$$SI = \frac{P \times R \times T}{100}$$

Substitute the known values:

$$600 = \frac{1200 \times 5 \times T}{100}$$

Step by step:

1. Multiply $1200 \times 5 = 6000$

2. Divide by 100: $6000 ÷ 100 = 60$

So:

$$600 = 60 \times T$$ $$T = \frac{600}{60} = 10$$

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✅ Step 4: Answer

Time = 10 years

Correct option: (a) 10 ✅

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💡 Quick Tip for Simple Interest Problems

1. Find SI first using $SI = A - P$

2. Use formula $SI = \frac{P \cdot R \cdot T}{100}$

3. Solve for the missing variable (here, T)