Jamia Millia Islamia MCA Time And Work Previous Year Questions (PYQs)
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A liquid container is usually filled up in 8 hours.
Due to a leak since the beginning, it took 2 hours more to fill the container.
The leak could empty the filled container in:
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2
3
4
Solution
Let leak alone empty the tank in x hours.
Normal filling rate = 1/8 per hour
With leak → filled in 10 hours → net rate = 1/10
So,
1/8 − 1/x = 1/10
⇒ 1/x = 1/8 − 1/10 = (5 − 4)/40 = 1/40
Hence, leak alone can empty in 40 hours.
If 100 cats kill 100 mice in 100 days, then 4 cats would kill 4 mice in how many days?
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Solution
Rate = 100 mice / (100 cats × 100 days) = 1/100 mouse per cat–day.
With 4 cats: daily kill = 4 × 1/100 = 1/25 mouse/day. For 4 mice: 4 ÷ (1/25) = 100 days.
Two pipes A and B can fill a tank in 12 min and 16 min respectively. Both are opened together; after how much time should B be closed so that the tank gets filled in 9 min?
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Solution
Rates A=1/12, B=1/16. Let B run for t minutes, then only A for (9−t).
t(1/12+1/16) + (9−t)(1/12) = 1 ⇒ t(7/48) + (9−t)(1/12) = 1 ⇒ t=4.
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