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Amal and Vimal together can complete a task in 150 days, while Vimal and Sunil together can complete the same task in 100 days. Amal starts working on the task and works for 75 days, then Vimal takes over and works for 135 days. Finally, Sunil takes over and completes the remaining task in 45 days. If Amal had started the task alone and worked on all days, Vimal had worked on every second day, and Sunil had worked on every third day, then the number of days required to complete the task would have been

CAT · 2024 · Quant Slot 2
Question:
Amal and Vimal together can complete a task in 150 days, while Vimal and Sunil together can complete the same task in 100 days. Amal starts working on the task and works for 75 days, then Vimal takes over and works for 135 days. Finally, Sunil takes over and completes the remaining task in 45 days. If Amal had started the task alone and worked on all days, Vimal had worked on every second day, and Sunil had worked on every third day, then the number of days required to complete the task would have been

Options

139
150
100
220
Answer: 139

Explanation:
Let work per day: A, V, S A + V = 1/150 → A = 1/150 − V V + S = 1/100 → S = 1/100 − V Total work: 75A + 135V + 45S = 1 Substitute A, S: 75(1/150 − V) + 135V + 45(1/100 − V) = 1 Solve: V = 1/300, A = 1/300, S = 1/150 Effective rate with alternate days: Amal: 1/300, Vimal: 1/600, Sunil: 1/450 Total rate = 1/300 + 1/600 + 1/450 = 13/1800 per day Total days = 1 ÷ (13/1800) = 1800/13 ≈ 139

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