Time, Work, and Projects

If A takes 12 days, then B's efficiency being 60% more means B works at 1.6x A's rate. So B takes 12/1.6 = 7.5 days. The phrase '60% efficient than that of A' is slightly awkward but mathematically leads to option B.

Total work = 6 × 36 = 216 painter-days. Work done in first 8 days: 6 × 8 = 48 painter-days. Remaining work = 216 - 48 = 168 painter-days. New team size = 6 + 18 = 24 painters. Days needed = 168/24 = 7 more days. Common mistake: calculating total days (8+7=15) instead of 'more days' required.

Using the formula M1D1 = M2D2: 2 people * 12 days = 6 people * X days. 24 = 6X, so X = 4 days. The more people working, the less time it takes.

This is an inverse proportion problem. Total man-days = 2 * 12 = 24. If 6 people work, the time taken is 24 / 6 = 4 days.

Total work = 30 men × 20 days × 9 hours/day = 5400 man-hours. This work must be completed by 40 men in 20 days. Hours per day = 5400/(40×20) = 6.75 hours = 7.5 hours. Work done is inversely proportional to men when days are fixed.

Bill paints 1/20 house per hour, George paints 1/30 per hour. Together they paint 1/20 + 1/30 = 5/60 = 1/12 house per hour. So time needed = 12 hours. Add rates, then take the reciprocal.

Let total days = d. A works for (d-10) days at rate 1/20 per day. B works for d days at rate 1/30 per day. Equation: (d-10)/20 + d/30 = 1. Solving: (3(d-10) + 2d)/60 = 1 → 5d-30 = 60 → 5d = 90 → d = 18. Check: A works 8 days (8/20 = 0.4), B works 18 days (18/30 = 0.6), total = 1 job.

Ben's rate = 1/8 work per day. Joe is 3× faster: rate = 3/8 per day. Ram is 5× faster: rate = 5/8 per day. Combined rate = 1/8 + 3/8 + 5/8 = 9/8 work per day. Time = Work ÷ Rate = 1 ÷ (9/8) = 8/9 days. This is approximately 0.89 days or about 21.3 hours.

Ben's rate: 20/5 = 4 drinks/min. Mary's rate: 20/10 = 2 drinks/min. Harry's rate: 20/15 = 4/3 drinks/min. Combined rate = 4 + 2 + 4/3 = 6 + 1.33 = 7.33 drinks/min. Time = 20 ÷ 7.33 = 2.73 minutes = 2 minutes + 0.73×60 seconds = 2 minutes 44 seconds (approximately).

A's efficiency is 50% more than B, so A's rate = 1.5 × (1/24) = 1/16. Combined rate = 1/24 + 1/16 = 5/48 work per day. Days needed = 48/5 = 9.6 days. Option D (16 days) is B's time alone, option C (6 days) would require faster workers, and option B (8 days) is too low.

Original work = 6 x 30 x 9 = 1620 man-hours. Ten times that is 16200 man-hours. The new schedule gives 25 x 8 = 200 hours per man, so men needed = 16200 / 200 = 81, matching option C.

Let A take x days. Then B takes x/2 and C takes x/3. Combined rate: 1/x + 2/x + 3/x = 1/2. So 6/x = 1/2, which means x = 12. B's time is x/2 = 6 days. C's time would be 4 days. A's time is 12 days.

This is an inverse proportion: (Men1 * Days1) = (Men2 * Days2). 36 * 18 = 27 * Days2. Days2 = (36 * 18) / 27. Dividing 18 and 27 by 9 gives (36 * 2) / 3 = 12 * 2 = 24 days.

A's rate is 1/10 and B's rate is 1/12. Combined rate = 1/10 + 1/12 = (6+5)/60 = 11/60. The time taken together is the reciprocal: 60/11 = 5 5/11 days. Other options represent calculation errors in the common denominator or reciprocal.