Mathematics

The elder daughter is 16 and will receive her amount at 21, so her money will earn interest for 5 years. The younger daughter is 8.5 and will receive her amount at 21, so her money will earn interest for 12.5 years. Let the elder daughter's principal be x and the younger daughter's principal be (35 - x) lakhs. Both amounts will be equal at 21 years: x + x*10%*5 = (35 - x) + (35 - x)*10%*12.5. Solving gives x = 15 lakhs.

The present worth is calculated by discounting each installment separately using simple interest at 8% per annum. Each installment is Rs. 702 (half of Rs. 1404). The first installment is due in 6 months, so its present value is 702 / (1 + 0.08 × 0.5) = Rs. 669.23. The second installment is due in 12 months, so its present value is 702 / (1 + 0.08 × 1) = Rs. 650. The total present worth is approximately Rs. 1319.23, which rounds closely to option A (Rs. 1325).

If the value of the article is taken as V, the man buys it for 10% less than its value, so the cost price (CP) is 0.9V. He sells it for 10% more than its value, so the selling price (SP) is 1.1V. The profit is SP - CP = 1.1V - 0.9V = 0.2V. The profit percentage is calculated on the cost price: (Profit / CP) × 100 = (0.2V / 0.9V) × 100 = 22.22%. Therefore, the gain percent is approximately 22.22%, which corresponds to option D ('more than 20% profit').

First, find the daily wheat consumption per man: 25 men eat 150 kg in 30 days, so total man-days = 25*30=750 man-days. Wheat per man-day = 150/750 = 0.2 kg. For 45 men eating 450 kg, total man-days = 450/0.2 = 2250 man-days. Number of days = 2250 man-days / 45 men = 50 days. However, this contradicts the options, so rechecking: Actually, 25 men eat 150 kg in 30 days, so daily consumption = 150/(25*30) = 0.2 kg per man per day. For 45 men and 450 kg, days = 450/(45*0.2) = 450/9 = 50 days. So the correct answer is 50 days, which corresponds to option B. The initial calculation was incorrect; the original correct_answer B is correct.

Initially, the total food supply is enough for 500 people for 6 days, so total food = 500 × 6 = 3000 person-days. After 2 days, 100 men desert, so 400 men remain. Food consumed in 2 days by 500 men = 500 × 2 = 1000 person-days. Remaining food = 3000 - 1000 = 2000 person-days. Now, 2000 person-days of food for 400 men means the food will last 2000 ÷ 400 = 5 days.

True discount (TD) is given by TD = (P × R × T) / 100, where P is the amount due, R is the rate, and T is the time in years. Here, TD = Rs.160, P = Rs.1760, R = 12%. Solving for T: 160 = (1760 × 12 × T) / 100, which gives T = 160 × 100 / (1760 × 12) = 0.7575 years, approximately 9 months.

The trader owes Rs. 10,028 due in 1 year but wants to settle the account after 3 months. This means the payment is effectively being made 9 months earlier than the due date. To find the amount to pay after 3 months, we calculate the present value of Rs. 10,028 discounted for 9 months at 12% per annum simple interest. Calculation: Time period for discounting = 1 year - 3 months = 9 months = 0.75 years Rate of interest = 12% per annum Present Value (PV) = Future Value / (1 + rate × time) = 10028 / (1 + 0.12 × 0.75) = 10028 / 1.09 = Rs. 9202.75 approximately. Among the given options, Rs. 9200 (option B) is the closest to the calculated present value. Therefore, the correct answer is option B. Option A (Rs. 9025.20) is not close to the correct discounted amount and seems incorrect based on the calculation.

Initially, the total food supply is enough for 500 men for 9 days, so total man-days of food = 500 × 9 = 4500. After 3 days, 100 more men join, so 400 men have consumed food for 3 days (400 × 3 = 1500 man-days). Remaining food = 4500 - 1500 = 3000 man-days. Now, 600 men (500 + 100) share the remaining food, so it will last 3000 ÷ 600 = 5 days. However, the question states 'At the end of 3 days 100 more men were admitted,' so the initial 3 days were for 500 men, not 400. Correcting: 500 men consume for 3 days = 1500 man-days, remaining food = 4500 - 1500 = 3000 man-days. Now 600 men consume the remaining food, so duration = 3000 ÷ 600 = 5 days. Therefore, the food will last 5 more days after the 3 days have passed, total 3 + 5 = 8 days. But the question asks 'How long will the food now last?' meaning after the 3 days, so the answer is 5 days. The original answer given was B (5 days), which is correct. Therefore, the correct answer is B.

True discount (TD) is given by TD = (P × R × T) / 100(100 + R × T/12), but for short periods, it can be approximated as TD = (P × R × T) / 100. Using the formula TD = (P × R × T) / 100, we get 122 = (2562 × R × 4) / 1200, solving for R gives approximately 13%.

The interest earned is Rs. 15,500 - Rs. 12,500 = Rs. 3,000. Using the simple interest formula I = (P × R × T) / 100, we have 3000 = (12500 × R × 4) / 100. Solving for R gives R = (3000 × 100) / (12500 × 4) = 6%. Therefore, the correct rate of interest is 6%, which corresponds to option D.