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Laxmi and Suhani together can do a piece of work in 12 days. Suhani and Megha together do it in 15 days. If Laxmi’s efficiency is twice that of Megha, Then the days required for Suhani alone to finish the work is:-1. 20 days 2. 16 days3. 17 days4. 15 days5. 25 days |
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Answer» Correct Answer - Option 1 : 20 days Given: Efficiency of Laxmi : Megha = 2 : 1 Laxmi and Suhani can do work together in 12 days. Suhani and Megha can do work together in 15 days. Concept Used: Time ∝ 1/efficiency Calculation: The ratio of efficiency of Laxmi and Meghna = 2 : 1 ⇒ The ratio of time taken by Laxmi and Meghna = 1 : 2 According to the question, Laxmi and Suhani can do work together 1 day = 1/12 Suhani and Megha can do work together in 1 days = 1/15 According to the question: Difference between Laxmi and Megha can do work together in 1 days ⇒ [(1/12) – (1/15)] ⇒ (5 – 4)/60 = 1/60 Let Laxmi alone complete the work in x days, Megha will do the same in 2x days. ⇒ [(1/x) – (1/2x)] = 1/60 ⇒ [(1/x) – (1/2x)] = 1/60 ⇒ [(2 – 1)/2x)] = 1/60 ⇒ 1/2x = 1/60 ⇒ x = 30 Suhani's 1 day's work, ⇒ [(1/12) – (1/30)] ⇒ [(5 – 2)/60)] ⇒ 3/60 = 1/20 ∴ Suhani alone to finish the work in 20 days. |
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