Amir alone can complete a job in 10 days and Salman alone can complete it in 8 days. Amir, Salman And Shahrukh together can complete the job in 3 days. A similar job but of a higher volume has been assigned to Salman & Shahrukh. The duo has decided to work on alternate days. Amir says that the work will be completed in an equal number of days if either of them starts the work. What is the minimum value of the ratio of the volume of a new job to that of the original one?

OA : Official Answer – 7:6

Assume work done is 120, so the efficiency of Amir and Salman be 12 and 15 respectively & Amir + Salman + Shahrukh be 40 (since they took 3 days.)

So the efficiency of Shahrukh is 40 – 12 – 15 = 13

Now the time to complete the work completed by Salman and Shahrukh working alternate days be same it means the work done is multiple of their sum of efficiency then [concept video]

Their efficiency sum = 15 + 13 = 28

We want a multiple of 28 but more than 120, which is 28*5 = 140

The required ratio of new work to old work = 140 : 120 = 7:6

Concept Video

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