Question

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

Answer 1

Hint: First we need to find the total amount of work in terms of days by taking the LCM of all the days \[40,\text{ }48\] and \[60\] . After that we need to assume a common unknown variable with which we will find the number of days each worked and equate it with the LCM of the number of days each worked as in the formula below:
 \[Sx+Tx+Ux=LCM\left( S,T,U \right)\] days
where \[Sx\] , \[Tx\] and \[Ux\] are the number of days worked by S,T and U.

Complete step-by-step answer:
 To find the total amount of work done in terms of number we use the LCM of days of work done by S,T and U. The LCM of the total work done is:
LCM of \[40,48,60\]
 \[\Rightarrow 240\]
Now the common variable of the number of days worked by S,T and U before two of leaving the work before timeline and one finishing till the end. Let the common unknown variable be x.
The work done by S is \[6x\] .
The work done by T is \[5\left( x-2 \right)\] .
The work done by U is \[4\left( x-5 \right)\] .
Now equating the total work done by S,U and T with the value of work done by all of them as:
 \[\Rightarrow 6x+5\left( x-2 \right)+4\left( x-5 \right)=240\]
 \[\Rightarrow 6x+5x-10+4x-20=240\]
 \[\Rightarrow 15x-10-20=240\]
 \[\Rightarrow 15x=240+30\]
 \[\Rightarrow x=18\]
Now the total money receive by all of them is Rs. \[10800\] and to divide the money amongst them we need to divide the work done by an individual to the total work done by all and then multiply it with the total amount received as shown below:
 \[\Rightarrow \dfrac{18}{240}\times 10800\]
 \[\Rightarrow \text{Rs}.4860\]
Therefore, the money received by S to complete his part of the job is \[\text{Rs}.4860\] .
So, the correct answer is “4860 Rs”.

Note: Another method to solve for the value of x is by placing the value of work done in terms of fraction as \[1\] and equating it with
 \[\Rightarrow \dfrac{x}{40}+\dfrac{1\left( x-2 \right)}{48}+\dfrac{1\left( x-5 \right)}{60}=1\] .