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Get access to the detailed solutions to the previous years questions asked in IIM IPMAT exam
We can take the work done by Amal, Vimal and Sunil to be A, V and S, respectively.
Let's take the total work they did to be T.
We are given the equations:
150A + 150V = T ...(1)
100V + 100S = T ...(2)
75A + 135V + 45S = T ...(3)
Adding (1) and (2), we get: 150A + 250V + 100S = 2T ...(4)
And multiplying (3) with 2 we get: 150A + 270V + 100S = 2T ...(5)
Subtracting (5) from (4), we get 10S = 20V or simply S = 2V
Using this in (2), we get the total work T to be 300V, and using that result in (1), we get A = V
Therefore, the work done by A, V and S equals V, V and 2V units per day.
Now, in the question, we are given work cycles.
To simplify the calculations, we should consider a time duration that is the LCM of the period taken by the three agents, which in this case would be 6
In 6 days, Amal will work for 6 days, doing 6V units of work.
Vimal will work for 3 days, doing 3V units of work.
Sunil will work for 2 days, doing 4V units of work.
So, in one 6-day cycle, 13V units of work will be done.
Dividing the total work (300V) by 13V we can see that in 23 cycles 299V units of work will be done.
These 23 cycles will be 23 × 6 = 138 days
The remaining 1V units of work will be done the next day.
Therefore, a total of 139 days will be required.