# 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:

A is twice efficient as B and together they do the same work in as much time as C and D together. If C and D can complete the work in 20 and 30 daysrespectively, working alone ,then in how many days A can complete the work individually:

 A) 12 days B) 18 days C) 24 days D) 30 days

Explanation:

A     +      B        =      C     +     D

|              |                 |             |

Ratio of efficiency         10x   +    5x               9x     +   6x

|________|                 |_________|

15x                           15x

Therefore , ratio of efficiency of A:C  =10:9

Therefore,  ratio of days taken by A:C = 9:10

Therefore, number of days taken by A = 18 days

4 2223
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

6 2131
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

1890
Q:

A contractor  undertook a project to complete it in 20 days which needed 5 workers to work continuously for all the days estimated. But before the start of the work the client wanted to complete it earlier than the scheduled time, so the contractor calculated that  he needed to increase 5 additional  men every 2 days to complete the work in the time the client wanted it:

If the work was further increased by 50% but the contractor continues to increase the 5 workers o every 2 days then how many more days are required over the initial time specified by the  client.

 A) 1 day B) 2 days C) 5 days D) None of these

Explanation:

Total work = 100+50 = 150man-days

In 8 days 100 man-days work  has been completed. Now on 9th and 10th day there will be 25 workers. So in 2 days they wll complete additional 50 man- days work. Thus the work requires 2 more days.

4 1813
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 = $\inline \fn_jvn \frac{1}{45}+\frac{1}{40}=\frac{17}{360}$)