Time and Work

Two pipes can fill a tank in $8 \mathrm{h}$ and $12 \mathrm{h}$ respectively whereas an escape pipe can empty it in $6 \mathrm{h}$. If the three pipes are opened at $1$ PM, $2$ PM and $3$ PM respectively, at what time will the tank be filled?

$25$ men and $15$ women can complete a piece of work in $12 \mathrm{days}$. All of them started working together and after working for $8 \mathrm{days}$ the women stop working. $25$ men completed the remaining work in $6 \mathrm{days}$. How many days will it take for completing the entire job if only $15$ women are put on the job?

$\mathrm{A}$ can do a piece of work in $40 \mathrm{days}$. He starts working, but having some other engagements he drops out after $5 \mathrm{days}$. Thereafter, $\mathrm{B}$ completes this work in $21 \mathrm{days}$. How many days would  $\mathrm{A}$ and $\mathrm{B}$ take to complete this work working together$?$

The ratio of the efficiency of a man to a woman is $4:3$. A group of $2$ men and$2$women together can complete a piece of work in $12$ days.

Quantity I: How many days a group of a man and three women will take to complete the same piece of work?

'x' men working $16$ hours a day can complete a work in $15$ days, while $(3x - 4)$men working $10$ hours a day can complete the same work in $9$ days. In how many days can $(x + 4)$men working $15$hours a day complete the same work?

Working together, Rajesh and Prakash can complete an assigned task in $20$ days. However, if Rajesh works alone and completes half the work and then Prakash takes over the task and completes the second half of the task, then the task will be completed in $45$days. How long will Rajesh take to complete the task if he worked alone? Assume that Prakash is more efficient than Rajesh

Working together, Rajesh and Prakash can complete an assigned task in $20$ days. However, if Rajesh works alone and completes half the work and then Prakash takes over the task and completes the second half of the task, then the task will be completed in $45$ days. How long will Rajesh take to complete the task if he works alone? Assume that Prakash is more efficient than Rajesh

A, B and C can complete a piece of work in $30$ days, $42$ days and $70$ days, respectively. All of them started the work together but A left the work after $8$ days while B left the work $14$ days before the completion of the remaining work. Find the total time taken to complete the whole work?

At their usual efficiency levels, A and B together finish a task in $12$ days. If A had worked half as efficiently as she usually does, and B had worked thrice as efficiently as he usually does, the task would have been completed in $9$ days. How many days would A take to finish the task if she works alone at her usual efficiency?

A, B and C can complete a work in $10, 12$ and $15$ days, respectively. They started the work together. But, A left the work before $5$ days of its completion. B also left the work $2$ days after A left. In how many days was the work completed?

A and B together can complete the work in $12$ days, and B and C together can complete the work in $15$ days. If C alone complete the half of the work in $10$ days, in how many days can A complete two-third of the work alone?

A alone can do a work in $20$ days. B is $25\%$ more efficient than A. A and B started working and worked for $4$ days; then C alone completed the remaining job in $22$ days. In how many days C alone can complete the entire job?

Five men and three women can do a piece of work in $12$ days, while three men and four women can do the same work in $15$days. An amount of $₹100$ is given to a woman for her contribution towards work per day. What is the total amount paid to five men and four women in a day?

Kavi and Pyare can complete the work in $50$ days and $40$ days, respectively. Both started working together, and after ‘$x$’ days, both left the job, and the remaining work was done by Mahi alone in $13$ days. Find the value of ‘x’ if Mahi is $25\%$ more efficient than Kavi

Amit and Sujit together can complete an assignment of Data entry in $5$ days. Sujit's speed is $80\%$ of Amit's speed and the total key depressions in the assignment are $5,76,000$. What is Amit's speed in key depressions per hour if they work for $4$ hours a day?

A and B can do a piece of work in $10$ days, B and C in $15$ days and C and A in $20$ days. They all work at it for $6$ days, and then A leaves, and B and C go on together for $4$ days more. If B then leaves, how long will C take to complete the work?

The work done by a woman in $8$ hours is equal to the work done by a man in $6$ hours and by a boy in $12$ hours. If working $6$ hours per day $9$ men can complete a work in $6$ days then in how many days can $12$ men, $12$ women and $12$ boys together finish the same work working 8 hours per day?

Ram decided to plough a farmland in $50$ days. He employed $50$ men in the beginning and $50$ more after $35$ days and completed the construction in stipulated time. If he had not employed the additional men, how many days behind schedule would it have been finished?

A and B working together, can do a piece of work in $4 \frac{1}{2}$ hours. B and C working together can do it in $3$ hours. C and A working together can do it in $2 \frac{1}{4}$ hours. All of them begin the work at the same time. Find how much time they will take to finish the piece of work?

Ramesh can finish a job in $20$ days. He worked for $10$ days alone and completed the remaining job working with Dinesh, in $2$ days. How many days would both Dinesh and Ramesh together take to complete the entire job?