**Exercise 7.5** 1. In what time ₹ 16001600 will amount to ₹ 17601760 at rate 5%5\% per annum at simple interest. 2. At what rate of simple interest will a sum double itself in two years. 3. Find simple interest and amount to be paid on ₹ 1500015000 at 5%5\% per annum after two years.

Answer: 1. 2 years 2. 50% per annum 3. Simple Interest = ₹1500, Amount = ₹16500

Step-by-step solution

Step 1: Solve Question 1: Find time

For Question 1, the principal P=₹1600P = \text{₹}1600, the amount A=₹1760A = \text{₹}1760, and the rate R=5%R = 5\%. The simple interest is SI=A−P=1760−1600=160\text{SI} = A - P = 1760 - 1600 = 160. Substituting into T=SI×100P×RT = \frac{\text{SI} \times 100}{P \times R}, we obtain T=2T = 2 years.

Step 2: Solve Question 2: Find rate of interest

For Question 2, the sum doubles itself in T=2T = 2 years, which means the amount A=2PA = 2P. Thus, the simple interest earned is SI=A−P=2P−P=P\text{SI} = A - P = 2P - P = P. Using the rate formula R=SI×100P×TR = \frac{\text{SI} \times 100}{P \times T}, we get R=1002=50%R = \frac{100}{2} = 50\%.

Step 3: Solve Question 3: Find simple interest and amount

For Question 3, the principal P=₹15000P = \text{₹}15000, the rate R=5%R = 5\%, and time T=2T = 2 years. Applying the simple interest formula SI=P×R×T100\text{SI} = \frac{P \times R \times T}{100}, we get SI=₹1500\text{SI} = \text{₹}1500. Adding this to the principal gives the total amount A=15000+1500=₹16500A = 15000 + 1500 = \text{₹}16500.

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