# Time and Work Questions

FACTS  AND  FORMULAE  FOR  TIME  AND  WORK  QUESTIONS

1. If A can do a piece of work in n days, then A's 1 day's work =$\inline \frac{1}{n}$

2. If A’s 1 day's work =$\inline \frac{1}{n}$, then A can finish the work in n days.

3. A is thrice as good a workman as B, then:

Ratio of work done by A and B = 3 : 1.

Ratio of times taken by A and B to finish a work = 1 : 3.

NOTE :

$\inline \dpi{100} \fn_jvn Efficiency \propto \frac{1}{number\; of\; time\; units}$

$\inline \dpi{100} \fn_jvn \therefore Efficiency \times time=constant\; work$

Hence, $\inline \dpi{100} \fn_jvn Required \; time = \frac{work}{efficiency}$

Whole work is always considered as 1, in terms of fraction and 100% , in terms of percentage.

In general, number of day's or hours = $\inline \fn_jvn \frac{100}{efficiency}$

Q:

Four pipes A,B, C and D can fill a cistern  in 20,25, 40 and 50 hours respectively.The first pipe A was opened at 6:00 am, B at 8:00 am, C at 9:00 am and D at 10:00 am. when will the Cistern be full?

 A) 4:18 pm B) 3:09 pm C) 12:15 pm D) 11:09 am

Explanation:

Efficiency of P= 5%

Efficiency of Q= 4%

Efficiency of R= 2.5%

Efficiency of S= 2%

$\inline&space;\left.\begin{matrix}&space;Till&space;\;&space;10\:&space;am&space;\;&space;pipe\;&space;P&space;\;&space;filled\;&space;20\;&space;percent\\&space;Till&space;\;&space;10\:&space;am&space;\;&space;pipe\;&space;Q&space;\;&space;filled\;&space;8\;&space;percent\\&space;Till&space;\;&space;10\:&space;am&space;\;&space;pipe\;&space;R&space;\;&space;filled\;&space;2.5\;&space;percent&space;\end{matrix}\right\}30.5$ %

Thus, at 10 am pipe P,Q and R filled 30.5% of the cistern.

Now, the time taken by P,Q,R and S together to fill the remaining capacity of the cistern

=$\inline&space;\frac{69.5}{13.5}$ = $\inline&space;\frac{139}{27}$ =5 Hours and 9 minutes(approx)

Therefore, total time =4 hrs + 5hrs 9 mins

= 9 hrs and 9 mins

It means cistern will be filled up at 3:09 pm

4 2659
Q:

Two pipes A and B can fill a cistern in 4 minutes and 6 minutes respectively . If these pipes are turned on alternately for 1 minute each how long will it take to the cistern to fill?

As the pipes are operating alternatively, thus their 2 minutes job is =$\inline \frac{1}{4}+\frac{1}{6}=\frac{5}{12}$

In the next 2 minutes the pipes can fill another $\inline \frac{5}{12}$ part of cistern.

$\inline \therefore$ In 4 minutes the two pipes which are operating alternatively will fill $\inline \frac{5}{12}+\frac{5}{12}=\frac{5}{6}$

Remaining part = $\inline 1-\frac{5}{6}=\frac{1}{6}$

Pipe A can fill $\inline \frac{1}{4}$ of the cistern in 1 minute

Pipe A can fill $\inline \frac{1}{6}$ of the cistern in =$\inline 4\times \frac{1}{6}=\frac{2}{3}$  min

$\inline \therefore$Total time taken to fill the Cistern

$\inline 4+\frac{2}{3}=4\frac{2}{3}$ minutes

2615
Q:

A tank has an inlet and outlet pipe. The inlet pipe fills the tank completely in 2 hours when the outlet pipe is plugged. The outlet pipe empties the tank completely in 6 hours when the inlet pipe is pluggeed.

If there is a lekage also which is capable of draining out the liquid from the tank at half of the  rate of outet pipe,them what is the time taken to fill the emty tank when both the pipes are opened?

 A) 3 hours B) 4 hours C) 5 hours D) None of these

Explanation:

Rate of leakage = 8.33% per hour

Net efficiency = 50 - (16.66 + 8.33)= 25%

Time required = 100/25 = 4 hours

7 2592
Q:

Amit can do a piece of work in 45 days, but Bharath can do the same work in 5 days less, than Amit, when  working alone. Amit and Bharath both started the work together but Bharath  left after some days and Amit finished the remaining work in 56 days with half of his efficiency but he did the work with Bharath with his complete efficiency. For how many days they had worked together?

 A) 6 B) 8 C) 9 D) 12

Explanation:

$\inline \fn_jvn \begin{matrix} & Amit& Bharath\\ No.of\: days& 45& 40\\ Efficiency& 2.22\: percent\left ( =\frac{1}{45} \right ) &2.5 \: percent\left ( =\frac{1}{40} \right ) \end{matrix}$

Amit did the work in 56 days = $\inline \fn_jvn 56\times \frac{1}{45\times 2}=\frac{28}{45}$

$\inline \fn_jvn \therefore$ Rest work $\inline \fn_jvn \left ( \frac{17}{45} \right )$ was done by Amit and Bharath = $\inline \fn_jvn \frac{17/45}{17/360}$ = 8 days

( since Amit and Bharath  do the work in one day = $\inline \fn_jvn \frac{1}{45}+\frac{1}{40}=\frac{17}{360}$)

5 2296
Q:

A and B can do a piece of work in 40 and 50 days. If they work at it an alternate days with A beginning in how many days, the work will be finished ?

(A+B)'s two days work = $\inline&space;\frac{1}{40}+\frac{1}{50}=\frac{9}{200}$

Evidently, the work done by A and B duing 22 pairs of days

i.e in 44 days = $\inline&space;22\times&space;\frac{9}{200}=\frac{198}{200}$

Remaining work = $\inline&space;1-\frac{198}{200}=\frac{1}{100}$

Now on 45th day A will have the turn to do $\inline&space;\frac{1}{200}$ of the work and this work A will do in $\inline&space;40\times&space;\frac{1}{100}-\frac{2}{3}$

$\inline&space;\therefore$ Total time taken = $\inline&space;44\frac{2}{5}$ daya