Time and Work — CDS Elementary Mathematics PYQs

Eight men and 24 women can finish a piece of work in one day while 12 men and 18 women can also finish it in one day. What is the time taken by 24 men and 72 women to finish the work?

$X$ can do a piece of work in 4 days and $Y$ can do the same piece of work in 6 days. Which of the following statements is/are correct?
I. If $X$ and $Y$ work alternately starting with $X$, then the piece of work will be finished on the fifth day.
II. If $X$ and $Y$ work alternately starting with $Y$, then the piece of work will be finished in less than 5 days.

Select the answer using the code given below:

12 men working 8 hours a day can completely build a wall of length 100 m, breadth 20 cm and height 5 m in 10 days. How many days will 16 men working 10 hours a day require to build a wall of length 200 m, breadth 60 cm and height 5 m?

If 15 men take 21 days of 8 hours each to do a piece of work, then what is the number of days of 6 hours each that 21 women would take, if 3 women would do as much work as 2 men ?

A and B working together can finish a piece of work in 12 days while B alone can finish it in 30 days. In how many days can A alone finish the work ?

If 5 men can do a piece of work in 10 days and 12 women can do the same work in 15 days, the number of days required to complete the work by 5 men and 6 women is

30 men can complete a job in 40 days. However, after 24 days some men out of the assigned 30 left the job. The remaining people took another 40 days to complete the job. The number of men who left the job is

4 goats or 6 sheep can graze a field in 50 days. 2 goats and 3 sheep will graze it in

A tap can fill a tub in 10 hours. After opening the tap for 5 hours it was found that a small outlet at the bottom of the tub was open and water was leaking through it. It was then immediately closed. It took 7 hours to fill the tub after closing the outlet. What time will be taken by the outlet to empty the full tub of water ?

Two pipes A and B can fill a tank in 60 minutes and 75 minutes respectively. There is also an outlet C. If A, B and C are opened together, the tank is full in 50 minutes. How much time will be taken by C to empty the full tank ?