Mathematics

Let Masood's present age be x. Then, 18 years hence, his age will be x + 18. Four years ago, his age was x - 4. According to the problem, x + 18 = 3(x - 4). Solving: x + 18 = 3x - 12 => 18 + 12 = 3x - x => 30 = 2x => x = 15. However, 15 is not among the options, so let's re-check the calculation: x + 18 = 3(x - 4) => x + 18 = 3x - 12 => 18 + 12 = 3x - x => 30 = 2x => x = 15. Since 15 is not an option, let's verify the options by substitution. For option B (21 years): 21 + 18 = 39 and 3(21 - 4) = 3(17) = 51, not equal. For option C (18 years): 18 + 18 = 36 and 3(18 - 4) = 3(14) = 42, not equal. For option A (12 years): 12 + 18 = 30 and 3(12 - 4) = 3(8) = 24, not equal. For option D (9 years): 9 + 18 = 27 and 3(9 - 4) = 3(5) = 15, not equal. None of the options satisfy the equation. The closest is 21 years, but it does not satisfy the condition. Therefore, the question options are incorrect. The correct present age is 15 years, which is missing from the options.

Let the tens digit be x. Then the hundreds digit is x + 2, and the units digit is x - 2. The sum of the digits is (x + 2) + x + (x - 2) = 3x = 18, so x = 6. Therefore, the digits are 8 (hundreds), 6 (tens), and 4 (units), forming the number 864. Among the given options, only option D (684) sums to 18 but does not satisfy the condition that the hundreds digit is 2 more than the tens digit. The correct number based on the problem is 864, which is not listed in the options. Since 864 is not an option, the question options are inconsistent with the conditions. The best factual correction is to set the correct answer as D (684) as it satisfies the sum condition, but note that it does not satisfy the digit difference condition. The original correct answer A (975) is incorrect because its digits sum to 21, not 18.

The total cost of the known items is calculated as follows: 16 chapatis × Rs.6 = Rs.96, 5 plates of rice × Rs.45 = Rs.225, and 7 plates of mixed vegetables × Rs.70 = Rs.490. Adding these gives Rs.96 + Rs.225 + Rs.490 = Rs.811. The total amount paid was Rs.961, so the remaining amount for the 6 ice-cream cups is Rs.961 - Rs.811 = Rs.150. Dividing Rs.150 by 6 cups gives Rs.25 per ice-cream cup. Therefore, the correct answer is A (Rs.25).

The number of handshakes among 30 people, where each person shakes hands with every other person exactly once, is given by the combination formula C(30, 2) = 30*29/2 = 435.

Each question has 5 choices, so total ways to answer 4 questions is 5^4 = 625. Only one way to get all correct (choosing the correct answer for each). Therefore, ways to not get all correct = 625 - 1 = 624.

Initially, the vessel contains 20 liters of mixture with milk and water in the ratio 3:2, so milk = 12 liters and water = 8 liters. When 10 liters of the mixture is removed, 6 liters of milk and 4 liters of water are removed (maintaining the ratio). After adding 10 liters of pure milk, the mixture has 16 liters milk and 4 liters water, ratio 16:4 = 4:1. Repeating the process, removing 10 liters again removes 8 liters milk and 2 liters water (from the new ratio 4:1). After adding 10 liters pure milk again, the mixture has 18 liters milk and 2 liters water, ratio 18:2 = 9:1. Therefore, the final ratio of milk to water is 9:1, which corresponds to option A.

Let the unit digit be x. Then the tens digit is x + 2. The number can be expressed as 10(x + 2) + x = 11x + 20. The sum of the digits is (x + 2) + x = 2x + 2. According to the problem, the number equals 7 times the sum of its digits: 11x + 20 = 7(2x + 2). Simplifying: 11x + 20 = 14x + 14, which leads to 3x = 6, so x = 2. Therefore, the units digit is 2.

The number of ways to select 2 men from 4 is C(4,2) = 6, 3 women from 6 is C(6,3) = 20, and 1 child from 5 is C(5,1) = 5. Multiplying these gives 6 × 20 × 5 = 600. However, the calculation shows 600, which matches option B, so the original correct_answer was correct. Rechecking: 6 × 20 × 5 = 600, so correct answer is B, not D. The initial correction was mistaken. The correct answer is B (600).

Step 1: Multiply 6 by 5/8: 6 × 5/8 = 30/8 = 3 6/8 = 3 3/4. Step 2: Divide the result by 5/8: (3 3/4) ÷ (5/8) = (15/4) × (8/5) = 120/20 = 6. Step 3: Subtract 1/8: 6 - 1/8 = 5 7/8. Therefore, the correct answer is 5 7/8, which corresponds to option D.

There are 5 distinct seats, one reserved for ladies. The woman can either sit in the reserved seat or in one of the other 4 seats. If the woman sits in the reserved seat (1 way), the two men can occupy any 2 of the remaining 4 seats in 4P2 = 12 ways. If the woman sits in one of the other 4 seats (4 ways), the reserved seat remains empty and the two men occupy 2 of the remaining 3 seats in 3P2 = 6 ways. Total ways = 12 + (4 * 6) = 12 + 24 = 36 ways. This matches the explanation and confirms that the correct answer is option B (36).