Practice Time & Work MCQs for HEC USAT-COM (Commerce) Mathematics — topic-wise sets with solved answers.
Q1. 8 men can dig a pit in 20 days. If a man works half as much again as a boy, then 4 men and 9 boys can dig a similar pit in:__________?
Answer: 16 days
Explanation: Since 1 man = 1.5 boys, 4 men + 9 boys = 6 + 9 = 15 boy-equivalents = 10 man-equivalents; total work = 8×20 = 160 man-days, so time = 160/10 = 16 days.
Q2. A and B together can complete a work in 12 days,. A alone can complete it in 20 days. If B does the work only for half a day daily, then in how many days A and B together will complete the work?
Answer: 15 days
Explanation: B works only half a day, so B's effective rate = 1/60 per day; combined rate = 1/20 + 1/60 = 4/60 = 1/15, giving 15 days.
Q3. Two pipes A and B can separately fill a tank in 12 and 15 minutes respectively. A third pipe C can drain off 45 liters of water per minute. If all the pipes are opened, the tank can be filled in 15 minutes. What is the capacity of the tank?
Answer: 540 liters
Explanation: Combined fill rate = 1/12 + 1/15 = 9/60; for tank to fill in 15 min the drain rate = 9/60 − 1/15 = 1/12 of tank/min = 45 L/min, so capacity = 45 × 12 = 540 litres.
Q4. Two pipes can separately fill a tank in 20 and 30 hours respectively. Both the pipes are opened to fill the tank but when the tank is full, a leak develops in the tank through which one-third of water supplied by both the pipes goes out. What is the total time taken to fill
Answer: 18 hrs
Explanation: Combined fill rate = 1/20 + 1/30 = 1/12; with 1/3 leaking, effective rate = 2/3 × 1/12 = 1/18; time = 18 hours.
Q5. A cistern has two taps which fill it in 12 min. and 15 min.respectively There is one outlet pipe in the cistern. When all the taps & pipe are opened, the empty cistern is full in 20 min. How long will the waste pipe (outlet) take to empty the full cistern?
Answer: 10 min
Explanation: Net fill rate with both taps open = 1/12 + 1/15 = 3/20 per min; in 20 min it fills 3 tanks but only 1 is needed, so the outlet drains 2 tanks in 20 min → empties 1 tank in 10 min.
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