Numerical: Unitary Method MCQ - Practice Questions with Answers

This is a direct proportion because identical notebooks have the same unit price. First find the price of 1 notebook: ₹245 ÷ 7 = ₹35. Now multiply by 11 to get the price of 11 notebooks: 35 × 11 = ₹385. So the statement that the price of 11 notebooks is ₹385 is the only correct statement among the options.

For the same tank, taps and time are inversely proportional. Total tap-hours = number of taps × time. With 15 taps, total work = 15 × 8 = 120 tap-hours. If 12 taps fill the same tank, required time = 120 ÷ 12 = 10 hours. So the assertion is true. The reason also states the correct inverse proportion relation, 15 × 8 = 12 × 10, and directly explains why the time is 10 hours.

Use the unitary method. Cost of 3 notebooks = ₹18, so cost of 1 notebook = 18 ÷ 3 = ₹6. Now multiply by each required quantity. For 5 notebooks, cost = 5 × 6 = ₹30, so a-2. For 7 notebooks, cost = 7 × 6 = ₹42, so b-1. For 9 notebooks, cost = 9 × 6 = ₹54, so c-3. The correct matching is a-2, b-1, c-3.

For the same work, workers and days are inversely proportional. Total work = number of workers × number of days. So the work equals 8 × 12 = 96 worker-days. If only 6 workers do this same work, required days = 96 ÷ 6 = 16. Therefore, 6 workers will take 16 days. The rate of each worker is assumed equal, so no other adjustment is needed.

Use machine-hours as the unit. In 7 hours, 4 machines give 4 × 7 = 28 machine-hours and produce 280 bottles. So, production in 1 machine-hour = 280 ÷ 28 = 10 bottles. Now 6 machines working for 5 hours give 6 × 5 = 30 machine-hours. Therefore, total bottles = 30 × 10 = 300. This uses both factors correctly. Hence, 6 machines will produce 300 bottles in 5 hours.