Time and Work

$A, B$ and $C$ together can complete the work in $24 \mathrm{days}$. $A$ alone complete the whole work is $45 \mathrm{days}$ more than $B$. $C$ alone complete the whole work in _____ $\mathrm{days}$ and the $A$ and $B$ together can complete the work in ______ $\mathrm{days}$.

$A) 120, 30$

$B) 80, 40$

$C) 100, 50$

$D) 150, 45$

A and B together can complete the job in $16$days, B and C together can complete the job in $20$ days. First A did the job for $6$days, B did the job for $9$ days and C completed the remaining job in $22$ days. Find the number of days in which C alone can complete the job?

$\mathrm{A}, \mathrm{B} \mathrm{and} \mathrm{C}$ can do a work in $12, 15 \mathrm{and} 20 \mathrm{days}$ respectively They start working together for sometime after $\mathrm{B}$ left after $2 \mathrm{days}$ of work $\mathrm{C}$ left then total work complete by $\mathrm{A}$ in $4 \mathrm{days}$. $\mathrm{A}$ gets $₹7000$ from whole work. Then find

$\mathrm{a})$ When $\mathrm{B}$ left

$\mathrm{b})$ Difference of amount of $\mathrm{B} \mathrm{and} \mathrm{C}$

Arul and Ovi together can complete the work in $12 \mathrm{days}$. Arul and Kavin together can complete a piece of work in $16 \mathrm{days}$ and with the help of Dinesh, they can complete the work in $12 \mathrm{days}$. The efficiency of Ovi is double of Dinesh. In how many days did Kavin alone complete the work?

$\mathrm{A}$ can complete the $\frac{1}{3}$ work in $4 \mathrm{days}$, $\mathrm{B}$ complete $\frac{1}{5}$ work in $3 \mathrm{days}$ and $\mathrm{C}$ works $\frac{3}{4}$ part of work in $15 \mathrm{days}$ alone. At first $\mathrm{A} \mathrm{and} \mathrm{B}$ work for $2 \mathrm{days}$ then $\mathrm{A}$ goes to leave $\mathrm{B}$ works for one day alone then $\mathrm{C}$ join with $\mathrm{B}$. After working two day together $\mathrm{B}$ goes. $\mathrm{C}$ working alone for one day then $\mathrm{A}$ return to work, work for two days together. Then $\mathrm{C}$ goes for leave and remaining work done by $\mathrm{A}$ alone. In how many days total work will be completed?

$A$ can do a piece of work in $12 \mathrm{days}$ and $B$ can do it in $15 \mathrm{days}$. They work together for $2 \mathrm{days}$, and then $B$ leaves and $A$ work for $2 \mathrm{days}$ then $C$ join with him to finish the work in $4 \mathrm{days}$. In how many days $C$ can alone complete the work?

Pipe $A$ and $B$ together can fill the tank in $15 \mathrm{hours}$. Pipe $B$ and $C$ together can fill the same tank in $20 \mathrm{hours}$. Pipe $B$ and $C$ started to fill the tank and after $3 \mathrm{hours}$ pipe $C$ is closed and pipe $A$ is opened. After $5 \mathrm{hours}$ from starting, pipe $B$ is closed. Then Pipe $A$ alone opened for $12 \mathrm{hours}$ to fill the tank completely. In how many hours pipe $A$ alone will take to fill the tank?

$6$ men can complete a piece of work in $12 \mathrm{days}, 8$ women can complete the same work in $18 \mathrm{days}$ whereas $18$ children can complete the piece of work in $10 \mathrm{days}$. $4$ men, $12$ women and $20$ children work for $2 \mathrm{days}$. If only men were to complete the remaining work in $1 \mathrm{day}$. How many men would be required totally?

Anurag can do a work in $12 \mathrm{days}$ and the ratio of efficiency of Veer to Ayushi is $8 : 9$. Anurag and Ayush together can do $2 \mathrm{units}$ more work in a day as Anurag and Veer together can do in a day and time taken by Veer and Ayush together to do same work is $\frac{72}{17} \mathrm{days}$. Find the time taken by Anurag and Ayush to complete the same work together?

$8$ men and $12$ women can complete the work in $10$ days, $4$ men and $9$ women complete the work in $14$ days. then find in how many days will $8$ men and 5 women can complete the$70\%$of task?

Amit can complete a piece of work in $‘x + 8’ \mathrm{days}$ while Bunty can complete the same work in $‘x + 18\text{'} \mathrm{days}$. If Amit and Bunty together can complete the whole work in $‘x’$, then find the time taken by Chandan, who is $75\%$ more efficient than Amit and Bunty together to complete $70\%$ of the work?

In the following question, find the value of three quantities given in the question and find the relation between them.

Quantity I: A, B and C together can complete a work together in $4$ days and Efficiency of D and C are in the ratio $1: 2$ respectively. The time taken by A and B together to complete the whole work is equal to the time taken by D and C together to complete the whole work. In how many days, D will complete the whole work alone?

Quantity II: X is $25\%$ more efficient than Y and $83\left(\frac{1}{3}\right)\%$ as efficient as Z. Time taken by X and Y together to do the work is $\left(\frac{2}{3}\right)$ days more than the time taken by persons Y and Z together. What is the time taken by X alone to do the whole work?

Quantity III: $15$ days

P and Q are $20\%$ and $25\%$ respectively more efficient than R who completes a job alone in $30 \mathrm{days}$. If R starts the work alone and is assisted by P and Q on every third day where Q works with$20\%$ more of his own efficiency, then what is the total time taken by them to complete the whole work?

In the following questions, find the value of three quantities given in the question and find the relation between them.

There are four friends namely Mukesh, Rahul, Sameer, and Mangesh. Mukesh can complete an assignment in $40 \mathrm{days}$. With the help of Mangesh, he can complete the assignment in $\frac{160}{9} \mathrm{days}$. Rahul and Sameer together can complete the assignment in $15 \mathrm{days}$. The efficiency of Rahul is thrice the efficiency of Sameer. The efficiency of Neelam is equal to the sum of the efficiencies of Mukesh and Rahul and the efficiency of Komal is equal to the sum of the efficiencies of Sameer and Mangesh.

Quantity$\mathrm{I}:$Find the time taken by Neelam and Komal to complete the assignment together.

Quantity$\mathrm{II}:$Rahul started the assignment and left after$5 \mathrm{days}$. Find the time taken by Sameer to complete the remaining part of the assignment.

Quantity $\mathrm{III}:$Find the time taken by Mukesh, Sameer, and Neelam to complete the assignment together.

Efficiency of taps A & B is $x \mathrm{litres}/\mathrm{hour}$ and$y \mathrm{litres}/\mathrm{hour}$ respectively. If A & B can fill a tank in $p \mathrm{hours}$ and $q \mathrm{hours}$ respectively and when both interchange their respective number of taken hours with their respective efficiency, then A & B takes $\left(p-14\right) \mathrm{hours}$ and $\left(q-7\right) \mathrm{hours}$ respectively to fill the same tank. If $(p-q) = 5 \mathrm{hours}$, find time taken by both taps to fill the tank together:

Efficiencies of two workers A and B are in the ratio  $7 : 5$ respectively and efficiencies of another two workers C and D are in the ratio $5 : 3$ respectively. If the ratio of total time taken by A and D to complete the whole work alone is $8 : 7$ respectively, then B is approximately what percent efficient than C? 

Arun, Sunita and Pooja can do a certain piece of work in $64 \mathrm{days}, 72 \mathrm{days} \mathrm{and} 96 \mathrm{days}$, respectively. All of them started working together but after _________ $\mathrm{days}$, Arun and Sunita left the job and the remaining work is done by Pooja alone in ________ $\mathrm{days}$.

The values given in which of the following options will fill the blanks in the same order in which is it given to make the above statement true:

$$\begin{gathered} \mathrm{A}. 24, 4 \\ \mathrm{B}. 11, 53.5 \\ \mathrm{C}. 18, 27 \\ \mathrm{D}. 12, 50 \end{gathered}$$

The ratio of the efficiency of A and B is $5:6$ working together they can complete the same work in $10$ days. B alone starts the work and leaves after $5$ days. then find in how many days A will finish the remaining work?

Abin and Babita started a work together and completed it in $4$ days more than the time taken by Chandan and Deepak together. Chandan who is $80\%$ as efficient as Eshita and can complete the whole work alone in $6$  days more than the time taken by Faizal alone. If Abin started work alone and on ninth day Deepak joins him, then the remaining work will be completed in $24$ days. Babita, Eshita and Faizal can complete the whole work together in $18$ days. Time taken by Abin alone is more than the time taken by Chandan alone.

From the given information in the above question, which of the following can be determined?

a) Time taken by Abin alone

b) Time taken by Chandan alone

c) Time taken by Babita alone

d) Time taken by Deepak alone

1) Ram completes a work in$20$ days and Shyam completes a work in $18$ days. When Ram and Syam work on alternate days starting from Ram then, how much time does it take to complete the work?