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Rohan takes twice the time taken by Sohan to complete a piece of work and half of the time taken by Mohan to complete the work. If all of them working together can complete the work in 12 days, in how many days Rohan and Sohan working together can complete that work?1. 10 days2. 12 days3. 14 days4. 16 days5. 20 days |
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Answer» Correct Answer - Option 3 : 14 days Calculation: Let the time taken by Sohan to complete the work = x days Then, time is taken by Rohan to complete the work = 2x days and Time is taken by Mohan to complete the work = 4x days According to the question: ⇒ \(12(\frac{1}{x}+{1}{2x}+{1}{4x})=1\) ⇒ \(\frac{4+2-1}{4x}=\frac{1}{12}\) ⇒ \(\frac{7}{4x}=\frac{1}{12}\) ⇒ x = 21 days Time was taken by Sohan to complete the work = x = 21 days Time taken by Rohan to complete the work = 2x = 2 x 21 = 42 days Time taken by Mohan to complete the work = 4x = 4 x 21 = 84 days Let the no of days taken by Rohan and Sohan to complete the work = p days According to the question: ⇒ \(p(\frac{1}{21}+{1}{42})=1\) ⇒ \(p\frac{1+2}{42}=1\) ⇒ p = 14 days ∴ The number of days by Rohan and Sohan to complete the work is 14 days. |
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