Manish, Nakul and Pintoo alone can complete a certain work in 21days, 28 days and 15 days, respectively. Manish and Pintoo started the work together while Nakul joined them after 5 days and worked with them till the completion of the work. For how many days did Nakul work?
Show answer & explanation
Correct answer: B
Explanation
The correct answer is Option 2 i.e 2
Manish, Nakul and Pintoo alone can complete a certain work in 21days, 28 days and 15 days, respectively.
Total work = L.C.M of 21, 28 and 15 = 420 units
⇒ Work done by Manish in a day = 420/21 = 20 units
⇒ Work done by Nakul in a day = 420/28 = 15 units
⇒ Work done by Pintoo in a day = 420/15 = 28 units
⇒ Work done by Manish and Pintoo in 5 days = 5( 20 + 28) = 240 units
⇒ Work left = 420 - 240 = 180 units
⇒ Work done by Manish, Pintoo and Nakul in a day = (20 + 15 + 28) = 63 units
⇒ Work done by them in 2 days = 2 × 63 = 126 units
⇒ Work left now = 180 - 126 = 54 units
⇒ Time taken to complete 54 units of work = 54/63 = 6/7
Thus, the total days for which Nakul work = 2 6/7 days