Question : X can do a piece of work alone in 15 days while Y alone can do it in 10 days. They worked together for 3 days and the remaining work was finished by Z in 1 day. If they get paid Rs. 4000 for the entire work, then what is the share of Z?
Option 1: Rs. 2000
Option 2: Rs. 1000
Option 3: Rs. 1200
Option 4: Rs. 800
Correct Answer: Rs. 2000
Solution :
One day's work of X = $\frac{1}{15}$
One day's work of Y = $\frac{1}{10}$
One day's work of X and Y = $\frac{1}{15}+\frac{1}{10}$ = $\frac{2+3}{30}$ = $\frac{1}{6}$
Three day's work of X and Y = $3\times\frac{1}{6}$ = $\frac{1}{2}$
Remaining work can be done by Z = $1-\frac{1}{2}$ = $\frac{1}{2}$
$\because$ Half of the work is done by Z alone and the other half is done by X and Y together.
$\therefore$ Share of Z = $\frac{4000}{2}$ = 2000
Hence, the correct answer is Rs. 2000.
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