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
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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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Question : X and Y together can do a piece of work in 30 days. Z alone can do it in 60 days. If they worked together, then in how many days they can finish the work?
Option 1: 50
Option 2: 25
Option 3: 45
Option 4: 20
Question : A alone can do a piece of work in 30 days. He worked at it for 5 days and then B alone finished the remaining work in 10 days. In how many days B alone can finish the entire work?
Option 1: 12 days
Option 2: 15 days
Option 3: 10 days
Option 4: 18 days
Question : X and Y together can do a work in 10 days. Y and Z together can do the same work in 15 days. Z and X together can do the same work in 12 days. In how many days can Z alone do the same work?
Option 1: 80 days
Option 2: 60 days
Option 3: 40 days
Option 4: 50 days
Question : Rimmi and Simmi can together finish a work in 40 days. They worked together for 30 days and then Simmi left. After another 30 days, Rimmi finished the remaining work alone. In how many days Rimmi alone can finish the work?
Option 1: 120 days
Option 2: 30 days
Option 3: 80 days
Option 4: 40 days
Question : X alone can finish a work in 18 days, and Y alone can finish the same work in 9 days. If X, Y, and Z together can finish the same work in 4 days, then in how many days Z alone can finish the work?
Option 2: 10 days
Option 3: 14 days
Option 4: 16 days
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