From the problem, we are given the simple interest SI = ₹ 1770, the rate of interest R = 8% per annum, and the time period T = 7.5 = (15)/(2) years. We need to find the principal sum P using the standard simple interest formula.

From the problem, we are given the simple interest SI = ₹ 1770, the rate of interest R = 8% per annum, and the time period T = 7.5 = (15)/(2) years. We need to find the principal sum P using the standard simple interest formula.

Multiple Choice Questions (MCQs) 13. The sum of money that will produce ₹ $1770$ as simple interest in $7\frac{1}{2}$ years as $8\%$ at per annum is (a) ₹ $2950$ (b) ₹ $3120$ (c) ₹ $2800$ (d) ₹ $3200$ 14. In what time will ₹ $1200$ amount to ₹ $1344$ at $6\%$ per annum? (a) $2\frac{1}{2}\text{ years}$ (b) $3\text{ years}$ (c) $2\text{ years}$ (d) $3\frac{1}{2}\text{ years}$ 15. In how much time would the simple interest on a certain sum be $0.125$ times the principal at $10\%$ per annum? (a) $1\frac{1}{4}\text{ years}$ (b) $1\frac{3}{4}\text{ years}$ (c) $2\frac{1}{4}\text{ years}$ (d) $2\frac{3}{4}\text{ years}$ 16. A person borrows ₹ $5000$ for $2$ years at $4\%$ p.a. simple interest. He lends it to another person at $6\frac{1}{4}\%$ p.a. for $2$ years. Find his gain in the transaction per year.

Answer: (a) ₹ 2950

Step-by-step solution

Step 1: Identify given values and formula

From the problem, we are given the simple interest $\text{SI} = \text{₹} 1770$ , the rate of interest $R = 8\%$ per annum, and the time period $T = 7.5 = \frac{15}{2}$ years. We need to find the principal sum $P$ using the standard simple interest formula.

Step 2: Rearrange formula to solve for Principal

To find the principal $P$ , we rearrange the simple interest equation by multiplying both sides by $100$ and dividing by $R \times T$ .

Step 3: Substitute the values and compute Principal

Substituting the values into the formula gives $8 \times \frac{15}{2} = 60$ in the denominator. Dividing $177000$ by $60$ yields $P = 2950$ . Therefore, the required sum of money is $\text{₹} 2950$ .

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