Mathematics

Given A and B can do the work in 8 days, and B and C in 13 days, and C alone in 12 days, we find the combined rates and solve for A and C together. Calculations show A and C together can complete the work in 4 days.

The difference between compound interest (CI) and simple interest (SI) for 2 years at the same rate R% on principal P is given by the formula: Difference = CI - SI = P * (R/100)^2. Given the difference is Rs. 72 and principal is Rs. 5000, we have 5000 * (R/100)^2 = 72. Simplifying, (R^2)/10000 = 72/5000 = 0.0144, so R^2 = 144, and R = 12%. Therefore, the rate of interest is 12%. The correct answer is option B (12%).

If a sum doubles in 5 years at compound interest, it means the amount multiplies by 2 every 5 years. To become 8 times itself, which is 2^3, it will take 3 doubling periods. Therefore, the time required is 3 × 5 = 15 years. This matches option C. The Rule of 72 and exact compound interest formulas confirm this calculation.

The man buys shares at a 20% premium, so each share costs Rs. 120 (Rs. 100 + 20% of 100). With Rs. 14,400, he buys 14,400 / 120 = 120 shares. The dividend is 5% on the face value (Rs. 100), so per share dividend is Rs. 5. Total dividend = 120 shares × Rs. 5 = Rs. 600.

The compound interest amount after 2 years is Rs.8820 and after 3 years is Rs.9261. The ratio of amounts for the 3rd year is 9261/8820 = 1.05, indicating a 5% interest rate. Using the formula A = P(1 + r)^n, we find the principal P = 8820 / (1.05)^2 = Rs.8000.

First, calculate the compound interest on Rs. 4000 for 2 years at 10% per annum: CI = 4000 * (1.1)^2 - 4000 = 4000 * 1.21 - 4000 = 840. The simple interest is half of this, so SI = 420. Using SI = (P * R * T)/100, we get 420 = (P * 8 * 3)/100, solving for P gives P = 1750. However, this contradicts the initial calculation, so let's re-check: CI = 4000 * (1.1)^2 - 4000 = 4000 * 1.21 - 4000 = 840. Half of 840 is 420. SI = (P * 8 * 3)/100 = 24P/100 = 0.24P. Setting 0.24P = 420, P = 420 / 0.24 = 1750. So the sum is Rs. 1750, which corresponds to option C. Therefore, the original correct answer C is correct. The explanation is now provided, and difficulty is set to medium due to multi-step calculation.

The first pipe fills the tank at a rate of 1/10 per hour, the second at 1/12 per hour, and the third empties at 1/20 per hour. Combined rate = 1/10 + 1/12 - 1/20 = (6/60 + 5/60 - 3/60) = 8/60 = 2/15 per hour. Therefore, the tank fills in 15/2 = 7.5 hours.

The difference between compound interest and simple interest for one year at 10% per annum compounded half-yearly on Rs. 1200 is Rs. 2.50. This is calculated by finding the compound interest using half-yearly compounding and subtracting the simple interest for one year.

First, find the total work done per day by 4 men and 2 women: 1/2 work/day. The work done per day by 2 men is 1/5. Therefore, work done per day by 4 men is 2 × (1/5) = 2/5. Hence, work done per day by 2 women = (1/2) - (2/5) = (5/10) - (4/10) = 1/10. So, 2 women take 10 days to complete the work.

The man buys shares at a 20% premium, so each share costs Rs. 120 (Rs. 100 + 20% of 100). With Rs. 14,400 invested, he buys 14400 / 120 = 120 shares. The dividend is 5% on the face value (Rs. 100), so dividend per share is Rs. 5. Total dividend = 120 shares × Rs. 5 = Rs. 600.