Practice GAT Quantitative Reasoning questions with answers and explanations.
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B's rate is 1/8 - 1/12 = 1/24.
Therefore, B alone needs 24 days.
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Total work is proportional to workers × hours × days.
So days = 8 × 6 × 15 ÷ (12 × 5) = 12.
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Worker-days remain constant for the same job.
Thus, 15 × 20 ÷ 12 = 25 workers.
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Twenty-four workers complete 1/4 in 10 days, so the remaining 3/4 needs 30 equivalent days at the same workforce.
Only 20 days remain, requiring 36 workers, so 12 extra are needed.
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Twice the efficiency means twice the daily work rate.
Therefore, A takes half of 18 days, which is 9 days.
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In four days, each works twice.
Completed work is 2/15 + 2/20 = 4/30 + 3/30 = 7/30.
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In 5 days, A completes 5/20 = 1/4 of the job.
Therefore, 3/4 remains.
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Let B's rate be 1 unit and A's 3 units, total 4 units.
A alone takes 8 × 4/3 = 32/3 days.
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If half the work takes 6 days, the full work takes twice as long.
Thus, the total time is 12 days.
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The machine produces 60/5 = 12 units per hour.
In 8 hours it produces 12 × 8 = 96 units.
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Their combined rate is 1/12 + 1/18 + 1/36 = 1/6.
Therefore, they finish in 6 days.
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If 40% takes 12 days, 10% takes 3 days.
The remaining 60% takes 18 days.
