Pushkin, Qutub and Ravinder together finish a task in 4 days. Ravinder and Samrat together finish it in 6 days. Qutub alone takes 20 days and Ravinder alone takes 10 days. In how many days can Pushkin and Samrat together finish the task?

Question

Rahul, Rakshita and Gurmeet, working together, would have taken more than 7 days to finish a job. On the other hand, Rahul and Gurmeet, working together would have taken less than 15 days to finish the job. However, they all worked together for 6 days, followed by Rakshita, who worked alone for 3 more days to finish the job. If Rakshita had worked alone on the job then the number of days she would have taken to finish the job, cannot be

Answer 1

Step 1: Take the total work as $\text{LCM}(4,6,20,10)=60$ units.
Step 2: Combined rate of Pushkin + Qutub + Ravinder $=\dfrac{60}{4}=15$ units/day.
Step 3: Qutub's rate $=\dfrac{60}{20}=3$ units/day; Ravinder's rate $=\dfrac{60}{10}=6$ units/day.
Step 4: Pushkin's rate $=15-3-6=6$ units/day.
Step 5: Combined rate of Ravinder + Samrat $=\dfrac{60}{6}=10$ units/day, so Samrat's rate $=10-6=4$ units/day.
Step 6: Pushkin + Samrat rate $=6+4=10$ units/day, so time $=\dfrac{60}{10}=6$ days.
\[\boxed{6\text{ days}}\]

Pushkin, Qutub and Ravinder together finish a task in 4 days. Ravinder and Samrat together finish it in 6 days. Qutub alone takes 20 days and Ravinder alone takes 10 days. In how many days can Pushkin and Samrat together finish the task?

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The Correct Option is C

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