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A and B can do a work in 60 days and 75 days respectively. Both A and B work together for 10 days. After that B leaves the work but A continues. then after 6 days, C also joins. Then after 24 days, work is completed. How much time it will take C alone to the complete their work?1. 130 days2. 120 days3. 122 days4. 125 days5. 121 days |
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Answer» Correct Answer - Option 2 : 120 days Given: A and B can do a work in 60 days and 75 days respectively Both A and B work together for 10 days. Calculation: Work done by A in 1 day = 1/60 Work done by B in 1 day = 1/75 Work done by both (A + B) in 1 day = (1/60 + 1/75) ⇒ (5 + 4)/300 ⇒ 9/300 = 3/100 Now, Work done by both (A + B) in 10 days = [10 × (3/100)] = 3/10 Remaining work = [1 – (3/10)] = 7/10 Work done by A in 6 day = [6 × (1/60)] = 1/10 Now, Remaining work = (7/10 – 1/10) ⇒ (7 – 1)/10 = (6/10) days According to the question: (A + C) × 6/10 = 24 ⇒ (A + C) = (24 × 10)/6 = 40 days Work done by both (A + C) in 1 days = 1/40 Work done by C in 1 day = (1/40 – 1/60) ⇒ (3 – 2)/120 = 1/120 ∴ Total time work done by c in 120 days. |
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