R. Gupta Solutions for Chapter: Time and Work, Exercise 1: EXERCISE

Two persons A and B can complete a piece of work in $8$ hours and $16$ hours, respectively. If they work at it alternately for an hour, A starting first, in how many hours will the work be finished?

Two taps A and B can fill a cistern in $12$ minutes and $15$ minutes, respectively. Both are opened together, but after $3$ minutes, tap A is turned off. After how much further time will the cistern be filled?

A and B working together can complete a piece of work in $12$ days. B and C working together can complete the same work in $16$ days. A worked at it for $5$ days, and B worked at it for $7$ days. C finished the remaining work in $13$ days. How many days would C alone take to complete it?

A cistern is filled by a tap in $3\frac{1}{2}$ hours. Due to a leak in the bottom of the cistern, it takes half an hour longer to fill the cistern. If the cistern is full, how long will it take the leak to empty it?

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

Two men undertake to do a piece of work for $₹1400$. The first man alone can do this work in $7$ days, while the second man alone can do this work in $8$ days. If working together, they complete this work in $3$ days with the help of a boy, how should the money be divided?

If $3$ men and $5$ women can do a piece of work in $8$ days, and $2$ men and $7$ boys can do the same work in $12$ days, find the number of boys who can do a piece of work equal to the work done by $10$ women.

A, B, and C can complete a piece of work in $20, 12$ and $18$ days, respectively. They start the work together, but A drops out after $4$ days, and B drops out $2$ days before the completion of the work. The work is finished in _____.