and and can complete work in 40,48 and 60 days respectively. They received Rs. 10800 to complete the work. They begin the work together but can complete work in 40,48 and 60 days respectively. They received Rs. 10800 to complete the work. They begin the work together but left 2 days before the completion of the work and U left 5 days before the completion of the work. left 2 days before the completion of the work and U left 5 days before the completion of the work. has completed the remaining work alone. What is the share of has completed the remaining work alone. What is the share of (in Rs.) from total money?

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8890 Rs.

5432 Rs.

4860 Rs.

4660 Rs.

answer is C.

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Detailed Solution

Concept- First, by calculating the LCM of all the days 40, 48, and 60, we must get the overall quantity of labor in terms of days. Following that, we must assume a common unknown variable with which we will determine the total number of days each employee worked and compare it to the LCM of those total days, as shown in the following formula:
Sx, Tx, and Ux are the number of days worked by S, T, and U, respectively, and Sx+Tx+Ux=LCM(S, T, U) days.
LCM of 40,48,60

The number of days that S, T, and U worked before two of them left the job early and one of them completed it to the end is now the shared variable. Let x serve as the universal unknown variable.
The work done by

is 6 x.
The work done by

.
The work done by

.
Now equating the total work done by S, U and

with the value of work done by all of them as:

The entire amount of money received by them all is now Rs. 10800, and in order to distribute it among them, we must first divide the amount of labor each person did by the sum of all their work, as shown below.

So, the money received by

to complete his part of the job is Rs. 4860 .
Hence, the correct answer is option 3.

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