R. S. Aggarwal Solutions for Chapter: Time and Work, Exercise 3: Exercise

$\mathrm{A},\mathrm{B}$ and $\mathrm{C}$ can do a work in $6,8$ and $12$ days respectively. If they do the work together and earn $₹2700,$ what is the share of $\mathrm{C}$ in that amount?

$12$men can finish a project in $20$ days. $18$women can finish the same project in $16$days and $24$children can finish it in $18$days. $8$women and $16$children worked for $9$days and then left. In how many days will $10$ men complete the remaining project?

A and B can do a piece of work in $72$ days, B and C can do it in $120$ days, A and C can do it in $90$ days. In what time can A alone do it?

$\mathrm{A}$ can do $\frac{1}{2}$ of a piece of work in $8$days while $\mathrm{B}$ can do $\frac{1}{3}$ of the same work in $8$days. In how many days can both do it together?

$\mathrm{A}$ does $\frac{1}{2}$ as much as $\mathrm{B},$ and $\mathrm{C}$does $\frac{1}{2}$ as much work as $\mathrm{A}$ and $\mathrm{B}$ together. If $\mathrm{C}$ alone can finish the work in $40$ days, then together all will finish the work in:

$\mathrm{A},\mathrm{B}$ and $\mathrm{C}$ can do a piece of work in $20$days, $30$ days and $60$ days, respectively. In how many days can all working together finish the work if A works daily, but $\mathrm{B}$and $\mathrm{C}$ assist on every third day?

$\mathrm{A}$ and $\mathrm{B}$ can do a piece of work in $18$ days, $\mathrm{B}$ and $\mathrm{C}$ can do it in $24$ days, $\mathrm{A}$ and $\mathrm{C}$ can do it in $36$ days. In how many days $\mathrm{B}$ alone can finish the work?

$\mathrm{A}$ and $\mathrm{B}$ can do a piece of work in $30$days while $\mathrm{B}$ and $\mathrm{C}$ can do the same work in $24$ days and $\mathbf{C}$ and $\mathrm{A}$ in $\mathbf{20}\mathbf{ }$days. They all work for $10$days and then $\mathrm{B}$ and $\mathrm{C}$ leave. How many days more will $\mathrm{A}$ take to finish the work?