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ATQ, Let the total work be 560 units (LCM of 140, 112 and 80) Amount of work done by N alone in one day = 560/140 = 4 units Amount of work done by V alone in one day = 560/112 = 5 units Amount of work done by R alone in one day = 560/80 = 7 units Amount of work done by N, V and R together in 12 days = 12 × (4 + 5 + 7) = 192 units Amount of work done by V alone in 16 days = 16 × 5 = 80 units Remaining work = 560 – 192 – 80 = 288 units Time taken by V and R together to complete 288 units work = 288/(7 + 5) = 24 days So, the number days for which V worked = 12 + 16 + 24 = 52 days
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