Mathematics

When two trains move in opposite directions, their relative speed is the sum of their speeds: 60 + 90 = 150 km/hr. Converting to m/s: 150 × (1000/3600) = 41.67 m/s. The total length to be crossed is 1.10 + 0.9 = 2.0 km = 2000 m. Time taken = distance / speed = 2000 / 41.67 ≈ 48 seconds. However, the question asks for the time taken by the slower train to cross the faster train, which is the same as the time for them to completely pass each other, so 48 seconds is correct. But the options given are 36, 45, 48, and 49, and the original correct answer was C (48). The calculation confirms 48 seconds is correct, so the original correct answer C is correct. The explanation was missing and is now provided. Difficulty is medium due to calculation complexity.

The total amount of food is enough for 1200 men for 10 days, which equals 1200 × 10 = 12,000 man-days of food. If there are only 1000 men, the food will last 12,000 ÷ 1000 = 12 days. Therefore, the correct answer is option B (12).

The statements "a > b" and "b > a" cannot both be true simultaneously because they contradict each other. Therefore, the situation cannot be evaluated as it is logically impossible.

The sum of the first n odd numbers is n squared. For n=70, the sum is 70² = 4900, which matches option A.

Zero is classified as an even number because it is divisible by 2 without any remainder (0 ÷ 2 = 0). It is also a whole number, as whole numbers include zero and all positive integers. However, since the question asks for a single classification and zero is definitively even by the standard mathematical definition, the most precise answer is that zero is an even number.

The problem involves two loans with different principals and interest rates over different time periods. The first loan is Rs. 725 lent for 12 months at rate R% per annum. The second loan is Rs. 362.50 lent after 8 months, so for 4 months, at twice the original rate (2R%). Calculating interest: - Interest from first loan = (725 * R * 1) / 100 = 7.25R - Interest from second loan = (362.5 * 2R * (4/12)) / 100 = (362.5 * 2R * 1/3) / 100 = (725R) / 300 = 2.4167R Total interest = 7.25R + 2.4167R = 9.6667R Given total interest = Rs. 33.50 So, 9.6667R = 33.50 R = 33.50 / 9.6667 ≈ 3.466%, which matches option A (3.46%). The original answer given as option B (4.5%) is incorrect based on the calculation. The explanation correctly shows the calculation and the correct answer is option A.

Starting from the retailer's selling price of Rs. 30.09 and knowing the retailer's profit is 25%, the retailer's cost price is Rs. 30.09 / 1.25 = Rs. 24.072. The wholesaler sells to the retailer at a 20% profit, so the wholesaler's cost price is Rs. 24.072 / 1.20 = Rs. 20.06. The manufacturer sells to the wholesaler at an 18% profit, so the manufacturer's cost price is Rs. 20.06 / 1.18 ≈ Rs. 17.0. Since the options are in whole rupees, Rs. 17 (option C) is closest, but the exact calculation shows Rs. 17.0, so option C is correct. However, rechecking calculations: 30.09 / 1.25 = 24.072, 24.072 / 1.20 = 20.06, 20.06 / 1.18 = 17.0. So the manufacturer's cost price is Rs. 17, matching option C. Therefore, the original correct answer C is accurate. The explanation has been added and difficulty set to medium due to multi-step calculation.

Given the amounts after 5 years (Rs. 9800) and 8 years (Rs. 12005) with simple interest, the difference in amount over 3 years is Rs. 12005 - Rs. 9800 = Rs. 2205, which is the interest for 3 years. Therefore, interest for 1 year = 2205 / 3 = Rs. 735. The principal can be calculated by subtracting the interest for 5 years from Rs. 9800: Principal = 9800 - (735 * 5) = 9800 - 3675 = Rs. 6125. The rate of interest per annum = (Interest per year / Principal) * 100 = (735 / 6125) * 100 ≈ 12%. This matches option C. The original answer 'B' was incorrect, and the explanation correctly supports option C as the right answer.

The origin in a coordinate system is the point where the x-axis and y-axis intersect, which is at (0,0). This is the standard definition in coordinate geometry.

First, calculate the total work in man-days using children or adults. Twelve children take 16 days, so total work = 12 × 16 = 192 child-days. Similarly, 8 adults take 12 days, so total work = 8 × 12 = 96 adult-days. Thus, 1 adult = 2 children in work rate. After 3 days, work done by 16 adults = 16 × 3 = 48 adult-days (or 96 child-days). Remaining work = 192 - 96 = 96 child-days. Now, 6 adults and 4 children work together. Converting adults to children: 6 adults = 12 children, total workers = 12 + 4 = 16 children equivalent. Days to finish remaining work = 96 / 16 = 6 days.