## 1st Bank clerk level Solved Question Set, 1st on Work time

This is the 1st solved question set of 10 practice problem exercise for Bank Clerk exams and the 1st on topic Work Time. It contains,

- 1st
**question set on Work time**for Bank Clerk level exams to be answered in 15 minutes (10 chosen questions) **Answers**to the questions, and- Detailed
**solutions**explaining**concepts**and showing**how to solve the problems quickly in mind**with minimum writing.

For maximum gains, the test should be taken first, and then the solutions are to be referred to. But more importantly, to absorb the concepts, techniques and reasoning explained in the solutions, one must solve many problems in a systematic manner using the conceptual analytical approach.

Learning by doing is the best learning. There is no other alternative towards achieving excellence.

### 1st Question set - 10 problems for Bank Clerk exams: 1st on topic Work time - answering time 15 mins

**Q1. **Six women and ten children working together take 6 days to complete a work. If six women working by themselves can complete the work in 10 days, how many days will ten children take to complete the work when working by themselves?

- 14 days
- 15 days
- 23 days
- 16 days
- None of the above

**Q2.** 56 men complete a job in 14 days. If the job is to be completed in 8 days, how many extra men will be required?

- 42
- 32
- 36
- 48
- 44

**Q3. **If 12 men complete one-third portion of a job in 8 days, how many days will 16 men take to complete the same job?

- 15 days
- 24 days
- 12 days
- 18 days
- None of the above

**Q4. **A can finish a work in 30 days. He worked alone for 6 days when B joined him. Together they could finish the remaining work in 9 days. In how many days B alone can finish the work while working alone?

- 12 days
- 14 days
- 15 days
- 10 days
- 18 days

**Q5. **A pipe can fill an empty tank in 5 hrs. Because of a leakage at the bottom of the tank the pipe takes $7\frac{1}{2}$ hrs to fill the tank. In what time will the leak empty the full tank with the filling pipe closed?

- 8 hrs
- 15 hrs
- 10 hrs
- 12 hrs
- 20 hrs

**Q6.** 16 men finish a work in 49 days. 14 men started working and in 8 days they could finish a certain portion of the work. If the remaining work is to be finished in 24 days, how many more men will be required?

- 21
- 18
- 28
- 16
- 14

**Q7.** In a tank, pipe A can fill $\frac{3}{5}$th of the tank in 27 hrs while pipe B can fill the empty tank completely in 30 hrs. In what time would the both pipes working together fill the empty tank completely?

- 16 hrs
- 18 hrs
- 20 hrs
- 27 hrs
- None of the above

**Q8.** A is twice as good a worker as B. A and B together complete a work in 28 days. In how many days will A alone do the same piece of work?

- 40 days
- 36 days
- 30 days
- 42 days
- None of the above

**Q9.** A and C can independently finish a piece of work in 18 days and 27 days respectively. A and C started working together and after 6 days B replaced them both. If B could finish the remaining work in 16 days, In how many days would B finish the full work while working alone?

- 40 days
- 34 days
- 36 days
- 32 days
- None of the above

**Q10.** 18 women complete a project in 24 days and 24 men complete the same project in 15 days. 16 women worked for 3 days and then they left. 20 men work for next 2 days and then they are joined by 16 women. in how many days will they complete the remaining work?

- $7\displaystyle\frac{3}{5}$
- $5\displaystyle\frac{2}{5}$
- $9\displaystyle\frac{1}{5}$
- $6\displaystyle\frac{1}{5}$
- None of the above

### Answers to the questions

**Q1. Answer:** Option b: 15 days.

**Q2. Answer:** Option a: 42.

**Q3. Answer:** Option d: 18 days.

**Q4. Answer:** Option e: 18 days.

**Q5. Answer:** Option b: 15 hrs.

**Q6. Answer:** Option e : 14.

**Q7. Answer:** Option b: 18 hrs.

**Q8. Answer:** Option d: 42 days.

**Q9. Answer:** Option c: 36 days

**Q10. Answer:** Option e: None of the above.

### 1st solution set - 10 problems for Bank clerk exams: 1st on topic Work time - answering time 15 mins

**Q1. **Six women and ten children working together take 6 days to complete a work. If six women working by themselves can complete the work in 10 days, how many days will ten children take to complete the work when working by themselves?

- 14 days
- 15 days
- 23 days
- 16 days
- None of the above

** Solution 1: Problem analysis and solving execution by using mandays technique**

With 6 women working by themselves for 10 days completing the work, the **amount of work in terms of womandays** is, 60 womandays. This measure of work amount is a powerfully effective concept and helps to solve many problems quickly and easily.

We will now employ * Work rate technique* to define per day work portion done by a woman as $W$, per day work portion done by a child as $C$ and the total work as, $R$.

By the first given condition then,

$6(6W+10C)=R$, a simple equation without fractions

Or, $36W+60C=R$.

As total work amound is 60 womandays,

$60W=R$,

Or, $36W=\displaystyle\frac{3}{5}R$, multiplying both sides by $\displaystyle\frac{3}{5}$.

Substituting,

$\displaystyle\frac{3}{5}R+60C=R$,

Or, $60C=\displaystyle\frac{2}{5}R$,

Or, $15\times{10C}=R$.

That is, 10 children will complete the work amount $R$ in 15 days.

**Answer:** Option b: 15 days.

**Key concepts used:** * Work time concept* --

*--*

**Mandays technique***.*

**Work rate technique -- Solving in mind**The problem could easily be solved in mind folllowing these concepts and techniques.

To know more about these very important techniques you may refer to our earlier articles,

**How to solve time and work problems in simpler steps type 1,**

**How to solve more time and work problems in simpler steps type 2.**

**Q2.** 56 men complete a job in 14 days. If the job is to be completed in 8 days, how many extra men will be required?

- 42
- 32
- 36
- 48
- 44

**Solution 2: Problem solving execution using mandays technique**

56 men complete the job in 14 days. So the total work amount is,

$R=56\times{14}$ mandays.

Then if the job is to be completed in 8 days, number of men required would be,

$\displaystyle\frac{56\times{14}}{8}=98$,

And extra men required,

$98-56=42$.

**Answer:** Option a: 42.

**Key concepts used:** **Mandays technique, work amount as mandays -- Inverse relationship between number of men and number of days of completing a work -- Solving in mind****.**

The problem is simple enough to be solved in mind quickly in a few tens of seconds.

**Q3. **If 12 men complete one-third portion of a job in 8 days, how many days will 16 men take to complete the same job?

- 15 days
- 24 days
- 12 days
- 18 days
- None of the above

**Solution 3: Problem analysis and execution**

12 men do one-third portion of the job in 8 days, and so will complete the whole job in $3\times{8}=24$ days (more job more time),

Or, 4 men will do the job in $3\times{24}=72$ days, men and days are inversely proportional, if you decrease men, days will be proportionally increased; number of men one-third of 12, so days required will be three times. Why 4? This is to use the unitary method easily with unit of 4 men which is the HCF of 12 and 16.

Or, 16 men will do the job in $\displaystyle\frac{72}{4}=18$ days, more men less time.

We could have easily solved this problen with mandays technique, but showed another approach by using unitary method on the inverse relationship between men and days.

#### Solution 3: Using work amount as mandays concept

12 men do one-third of the job in 8 days, so the work amount is, $12\times{3}\times{8}$ mandays.

Then 16 men will do the job in,

$\displaystyle\frac{12\times{3}\times{8}}{16}=18$ days.

As mandays technique is a higher level technique, solution will always be faster.

**Answer:** Option d: 18 days.

**Key concepts used: Men and days inverse proportionality with fixed work, **

*Worker to work time inverse proportionality*

*-- Work amount as mandays -- Unitary method -- Solving in mind*

**.****Q4. **A can finish a work in 30 days. He worked alone for 6 days when B joined him. Together they could finish the remaining work in 9 days. In how many days B alone can finish the work while working alone?

- 12 days
- 14 days
- 15 days
- 10 days
- 18 days

**Solution 4: Problem solving using work portion done in a day concept**

A can finish the work in 30 days,

So he finishes $\displaystyle\frac{1}{30}$th of work in 1 day,

Or, finishes $\displaystyle\frac{6}{30}=\frac{1}{5}$th of the work in 6 days. This is the time when B joined him.

In 9 days they finish the remaining work.

In these 9 days A did, $\displaystyle\frac{9}{30}=\frac{3}{10}$th of the remaining $\displaystyle\frac{4}{5}$th work.

So B did in 9 days,

$\displaystyle\frac{4}{5}-\displaystyle\frac{3}{10}=\displaystyle\frac{1}{2}$ of the work.

Thus to do the full work B should take, $2\times{9}=18$ days.

We have used the very basic unitary method and leftover work concepts. We have bypassed working together process. We could do that because while working together both workers work independently.

**Answer:** Option e: 18 days.

**Key concepts used: Work time concepts -- Work portion to number of days direct proportionality, work time proportionality -- Unitary method -- Work rate -- Leftover work -- Solving in mind**

**.**Folllowing the simple to understand process solution could be reached wholly in mind.

**Q5. **A pipe can fill an empty tank in 5 hrs. Because of a leakage at the bottom of the tank the pipe takes $7\frac{1}{2}$ hrs to fill the tank. In what time will the leak empty the full tank with the filling pipe closed?

- 8 hrs
- 15 hrs
- 10 hrs
- 12 hrs
- 20 hrs

**Solution 5: Problem solving using fill rate and emptying rate in portion of tank filled in 1 hour**

By using fill rate and emptying rate of the pipe and the leak in terms of portion of tank filled or emptied in 1 hour, when the two work together we have,

$\displaystyle\frac{1}{5}-\displaystyle\frac{1}{L}=\displaystyle\frac{2}{15}$, where it is assumed that leak can empty the full tank in $L$ hrs,

Or, $\displaystyle\frac{1}{L}=\frac{1}{15}$.

So the leak working alone can empty the full tank in 15 hrs.

**Answer:** Option b: 15 hrs.

*Key concepts used:* **Fill rate in terms of portion of tank filled in 1 hour as inverse of hrs required to fill the tank, time work portion inverse proportionality as rate -- Leak rate to be subtracted from fill rate to get efffective fill rate in 1 hr -- Working together -- Pipes and cisterns problems -- Solving in mind****.**

**Q6.** 16 men finish a work in 49 days. 14 men started working and in 8 days they could finish a certain portion of the work. If the remaining work is to be finished in 24 days, how many more men will be required?

- 21
- 18
- 28
- 16
- 14

**Solution 6: Problem analysis and solution by work amount as mandays concept and leftover work concept**

16 men can finish a work in 49 days.

So total mandays measure of the work is, $16\times{49}$ mandays.

Out of this work, 14 men working for 8 days then finished, $8\times{14}$ mandays work.

Leftover work is then,

$16\times{49}-8\times{14}=16\times{42}$ mandays.

To finish this leftover work in 24 days then a total of,

$\displaystyle\frac{16\times{42}}{24}=28$ men will be required. This will be an additional 14 men to existing 14 men.

**Answer:** Option e : 14.

**Key concepts used:** ** Work amount as mandays -- Mandays technique -- Leftover work -- Delayed evaluation technique**.

To speed up solution by avoiding calculations as late as possible, we write down the products only and used factor cancellation to transform the calculations to simple ones. This is delayed evaluation technique.

**Q7.** In a tank, pipe A can fill $\frac{3}{5}$th of the tank in 27 hrs while pipe B can fill the empty tank completely in 30 hrs. In what time would the both pipes working together fill the empty tank completely?

- 16 hrs
- 18 hrs
- 20 hrs
- 27 hrs
- None of the above

**Solution 7: Problem analysis and solution by fill rate and working together concept**

Fill rate in terms of portion of tank filled in 1 hr by pipe A is,

$\displaystyle\frac{\frac{3}{5}}{27}=\frac{1}{45}$.

Similarly fill rate of pipe B is simply $\displaystyle\frac{1}{30}$.

In 1 hr portion of tank filled up by the two working together is then,

$\displaystyle\frac{1}{45}+\displaystyle\frac{1}{30}=\displaystyle\frac{1}{18}$

In 18 hrs two pipes working together will fill the empty tank.

**Answer:** Option b: 18 hrs.

** Key concepts used:** *Fill rate of filling pipes in terms of portion of tank filled up in 1 hr -- Working together concept enables adding up fill rates of two pipes to get the portion of tank filled in 1 hr by both of them working together -- Solving in mind.*

By following the above steps the problem could easily be solved in mind without any writing.

**Q8.** A is twice as good a worker as B. A and B together complete a work in 28 days. In how many days will A alone do the same piece of work?

- 40 days
- 36 days
- 30 days
- 42 days
- None of the above

** Solution 8: Problem analysis and execution by Worker equivalence and Work rate technique**

If work portion done in a day by A and B are $A$ and $B$, using worker equivalence concept,

$A=2B$,

Or, $B=\displaystyle\frac{1}{2}A$.

By the second statement using work rate technique of defining work rate as the variable,

$28(A+B)=R$, $R$ is assumed to be the work amount,

Or, $28A + 14A=R$, substituting $B=\displaystyle\frac{1}{2}A$

Or, $42A=R$.

A alone will complete the work in 42 days.

**Answer:** Option d: 42 days.

**Key concepts used:** **Work rate technique as portion of work done in a day as the variable -- Working together concept -- Worker comparison regarding their work capacity, worker equivalence -- Solving in mind.**

By using the above concepts and techniques, the problem could easily be solved in mind.

**Q9.** A and C can independently finish a piece of work in 18 day and 27 days respectively. A and C started working together and after 6 days B replaced them both. If B could finish the remaining work in 16 days, in how many days would B finish the full work while working alone?

- 40 days
- 34 days
- 36 days
- 32 days
- None of the above

**Solution 9: Problem analysis and execution by Work rate as work portion done in a day and Working together concept by adding work rates**

We will use the direct work rate concept here instead of the work rate technique with work rate as the worker variable.

Work portion done by A and C working together for 6 days is,

$\displaystyle\frac{6}{18}+\displaystyle\frac{6}{27}=\displaystyle\frac{5}{9}$, multiplying work rates of A and B by 6 on the LHS to take care of 6 days work.

Rest $\displaystyle\frac{4}{9}$ portion of the work is finished by B alone in 16 days.

So B will finish the **whole work** in, $\displaystyle\frac{16}{\displaystyle\frac{4}{9}}=36$ days, by unitary method as work portion done is directly proportional to work days required for completion of the work.

**Answer:** Option c: 36 days.

**Key concepts used:** * Work rate concept -- Working together concept* --

**Unitary method -- Work portion done to work days required direct proportionality, work time proportionality -- Solving in mind.**The problem could easily be solved in mind this time using direct work rate concept instead of work rate technique with work rates as worker variables.

**Q10.** 18 women complete a project in 24 days and 24 men complete the same project in 15 days. 16 women worked for 3 days and then they left. 20 men work for next 2 days and then they are joined by 16 women. in how many days will they complete the remaining work?

- $7\displaystyle\frac{3}{5}$
- $5\displaystyle\frac{2}{5}$
- $9\displaystyle\frac{1}{5}$
- $6\displaystyle\frac{1}{5}$
- None of the above

**Solution 10: Problem analysis and execution by work amount as mandays and work rate concept as work portion completed in a day**

Work rate of a woman is, $\displaystyle\frac{1}{18\times{24}}$ portion of work per day, as whole work amount is $18\times{24}$ womandays.

Work rate of a man is, $\displaystyle\frac{1}{24\times{15}}$ portion of work per day, as whole work amount is $24\times{15}$ mandays.

So, 16 women working for 3 days completed $48\times{\displaystyle\frac{1}{18\times{24}}}=\displaystyle\frac{1}{9}$ portion of work, 48 womandays multiplied by one woman work rate per day.

Similarly, 20 men doing 2 days work complete further, $40\times{\displaystyle\frac{1}{24\times{15}}}=\displaystyle\frac{1}{9}$ portion of work, 40 mandays multiplied by one man work rate per day.

Rest, $\displaystyle\frac{7}{9}$ portion of work will be done by 20 men and 16 women in, say, $x$ number of days, where,

$20x\times{\displaystyle\frac{1}{24\times{15}}}+16x\times{\displaystyle\frac{1}{18\times{24}}}=\displaystyle\frac{7}{9}$

Or, $\displaystyle\frac{x}{18}+\displaystyle\frac{x}{27}=\displaystyle\frac{7}{9}$,

Or $5x=42$,

Or, $x=8\frac{2}{5}$ days.

**Answer: **Option e: None of the above.

**Key concepts used:** **Work rate concept -- Work amount as mandays -- Leftover work concept -- Working together concept -- Delayed evaluation technique.**

To ensure accuracy with fair amount of calculations, we needed to write down the intermediate products using delayed evaluation technique cancelling out the common factors at the end.

#### Alternate solution by Work amount as mandays and Worker equivalence concepts

By given statement, total work amount for men in mandays and for women in womandays will be,

$18\times{24}\text{ womandays}=24\times{15}\text{ mandays}$

Or, $6\text{ womandays}=5\text{ mandays}$.

In other words, 5 men can be substituted by 6 women (and vice versa) as their work done in same work period are same.

So in the first phase of 48 womandays of work can be replaced by 40 mandays work. In the second phase also 40 mandays work is done, totalling 80 mandays work in two phases. This is equivalent to,

$\displaystyle\frac{80}{24\times{15}}=\frac{2}{9}$th of the total work. The leftover work is then, $\displaystyle\frac{7}{9}$th of total work.

In the last phase of work, replacing 20 men by 24 women, effectively 40 women work to finish the leftover work. This period will then be,

$\displaystyle\frac{7}{9}\times{\displaystyle\frac{18\times{24}}{40}}$

$=\displaystyle\frac{42}{5}$

$=8\frac{2}{5}$ days.

Choose your method.

Solving a problem in more than one way is * many ways technique*, and practice of that improves general problem solving ability.

### Useful resources to refer to

#### Concept tutorials and quick methods to solve work time problems

**How to solve Arithmetic problems on Work-time, Work-wages and Pipes-cisterns**

**How to solve Work-time problems in simpler steps type 1**

**How to solve Work-time problem in simpler steps type 2**

**How to solve difficult Work time problems in simpler steps, type 3**

#### Bank clerk level solved question sets on work time

**Bank clerk level solved question set 1 work time 1**

**Bank clerk level solved question set 2 work time 2**

You may also refer to **all Efficient Work time problem solving and Work time Question and Solution sets on other exams** in, * Time and Work problems*.