Manoj can complete a work in 15 days working 8 hours in a day and Santosh can complete it in 10 days working 9 hours in a day. If Manoj and Santosh together start working for 6 hours per day, in how many days will they complete the work?

Let the efficiency of Manoj be M and that of Santosh be S. Total work to be done (according to Manoj) = 15 × M × 8   Total work to be done (according to Santosh) = 10 × S × 9 Work done by both are the same, => 15 × M × 8  = 10 × S × 9 => M/S = 3/4 Let the efficiency of Manoj and Santosh be 3 and 4 respectively. Working together, total efficiency = 3 + 4 = 7  Let them finish the work by D days. Total work to be done = 15 × M × 8 = 15 × 3 × 8  => 7 × D × 6 = 15 × 3 × 8  Time taken = 360/42 = 8 (4/7) days