## 2nd Bank clerk level Solved Question Set, 2nd on Work time

This is the 2nd solved question set of 10 practice problem exercise for Bank Clerk exams and the 2nd on topic Work Time. It contains,

- 2nd
**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.

### 2nd Question set - 10 problems for Bank Clerk exams: 2nd on topic Work time - answering time 15 mins

**Q1. **18 men can complete a piece of work in 72 days, 12 women complete the same piece of work in 162 days and 9 children complete it in 360 days. Then in how many days can 4 men, 12 women and 10 children working together complete the work?

- 96 days
- 68 days
- 124 days
- 81 days
- None of the above

**Q2.** Two taps A and B can fill a tank in 16 hours and 12 hours respectively. If both taps are opened simultaneously and after two hours tap A is closed, how much time will tap B take to fill the remaining portion of the tank (in hours)?

- $7$
- $9\frac{1}{2}$
- $6$
- $8\frac{1}{2}$
- $5\frac{1}{2}$

**Q3. **When 25 men work for only 3 days, $\displaystyle\frac{4}{5}$th of the work remains unfinished. How much work will remain unfinished if 15 men work for only 4 days?

- $\displaystyle\frac{9}{10}$
- $\displaystyle\frac{11}{12}$
- $\displaystyle\frac{21}{25}$
- $\displaystyle\frac{13}{14}$
- $\displaystyle\frac{12}{13}$

**Q4. **P, Q and R each working alone can finish a job in 27, 33 and 45 days respectively. P starts working alone for 12 days, then Q takes over from P and work for 11 days. At this stage R takes over from Q and completes the remaining work. In how many days was the whole work completed?

- 33 days
- 35 days
- 37 days
- 39 days
- 31 days

**Q5. **A and B together can complete a given work in 9 days. Working alone A takes 24 days less than B working alone to complete the work. In how many days will B working alone complete the work?

- 36 days
- 45 days
- 54 days
- 42 days
- None of the above

**Q6.** A group of workers could complete a piece of work in 84 days. If there were 6 more workers, it would have taken 12 days less to finish the piece of work. What was the original strength of workers?

- 40
- 32
- 48
- 36
- 42

**Q7.** 18 men can complete a piece of work in 24 days and 12 women can complete the same piece of work in 32 days. 18 men start working and after a few days, 4 men leave the job and 8 women join. If the remaining work was completed in $15\displaystyle\frac{15}{23}$ days, after how many days did the four men leave?

- 2 days
- 5 days
- 4 days
- 6 days
- 8 days

**Q8.** A work can be finished by 36 workers in 14 days. If the work were to be finished in 8 days, how many additional workers would be required?

- 29
- 31
- 23
- 33
- 27

**Q9.** A alone can finish a work in 42 days. B is 20% more efficient than A and C is 40% more efficient than B. In how many days B and C working together can finish the same piece of work?

- $12\displaystyle\frac{11}{12}$ days
- $11\displaystyle\frac{5}{12}$ days
- $15\displaystyle\frac{1}{12}$ days
- $14\displaystyle\frac{7}{12}$ days
- $13\displaystyle\frac{5}{12}$ days

**Q10.** Two pipes can fill a tank in 12 hrs and 16 hrs respectively. A third pipe can empty the tank in 30 hrs. If all the three pipes were opened and function simultaneously, in how many hrs would the tank be full?

- $10\displaystyle\frac{4}{9}$ hrs
- $7\displaystyle\frac{2}{9}$ hrs
- $9\displaystyle\frac{1}{9}$ hrs
- $9\displaystyle\frac{5}{9}$ hrs
- $8\displaystyle\frac{8}{9}$ hrs

### Answers to the questions

**Q1. Answer:** Option d: 81 days.

**Q2. Answer:** Option d: $8\displaystyle\frac{1}{2}$.

**Q3. Answer:** Option c: $\displaystyle\frac{21}{25}$.

**Q4. Answer:** Option a: 33 days.

**Q5. Answer:** Option a: 36 days.

**Q6. Answer:** Option d : 36.

**Q7. Answer:** Option c: 4 days.

**Q8. Answer:** Option e: 27.

**Q9. Answer:** Option d: $14\displaystyle\frac{7}{12}$ days.

**Q10. Answer:** Option e: $8\displaystyle\frac{8}{9}$ hrs.

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

**Q1. **18 men can complete a piece of work in 72 days, 12 women complete the same piece of work in 162 days and 9 children complete it in 360 days. Then in how many days can 4 men, 12 women and 10 children working together complete the work?

- 96 days
- 68 days
- 124 days
- 81 days
- None of the above

** Solution 1: Problem analysis and solving by using work rate per day of a man, a woman and a child**

We decide to adopt the straightforward path of evaluating individual work portion done in a day for 1 man, 1 woman and 1 child and use these work rates to find the solution when they work together. This is standard use of work rate per unit time concept and working together concept.

From the given statements,

the per day work portion done by a man is, $\displaystyle\frac{1}{18\times{72}}$,

the per day work portion done by a woman is, $\displaystyle\frac{1}{12\times{162}}$, and

the per day work portion done by a child is, $\displaystyle\frac{1}{9\times{360}}$.

The denominators represent the total work amount in terms of mandays, womandays and childdays respectively.

So when 4 men, 12 women and 10 children work together, they complete the portion of total of work,

$\displaystyle\frac{4}{18\times{72}}+\displaystyle\frac{12}{12\times{162}}+\displaystyle\frac{10}{9\times{360}}$

$=\displaystyle\frac{1}{18^2}+\displaystyle\frac{1}{9\times{18}}+\displaystyle\frac{1}{18^2}$

$=\displaystyle\frac{4}{18^2}$

$=\displaystyle\frac{1}{81}$.

So the piece of work will be completed by the three teams working together in 81 days.

**Note:** We have kept the factors in the products as they are till we could simplify by factor cancellation. As a rule we follow this **delayed evaluation technique** that takes away the need for multiplying and again factorizing to a great extent.

**Answer:** Option d: 81 days.

**Key concepts used:** * Work rate per unit time concept* --

**.**

*Working together concept -- Delayed evaluation technique*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.** Two taps A and B can fill a tank in 16 hours and 12 hours respectively. If both taps are opened simultaneously and after two hours tap A is closed, how much time will tap B take to fill the remaining portion of the tank (in hours)?

- $7$
- $9\frac{1}{2}$
- $6$
- $8\frac{1}{2}$
- $5\frac{1}{2}$

**Solution 2: Problem solving execution using fill rate concept**

Fill rate of a pipe is the portion of the tank it is filling in 1 hour. This is equivalent to work rate per unit time for a worker. Pipe is the worker here.

If more than 1 pipe work to fill up or empty a tank, their individual fill rates can be added up to get the **effective fill rate in 1 hour (which is portion of tank filled up by all of the pipes together)** when all pipes work together.

In our problem effective fill rate or portion of tank filled in 1 hour when both the pipes are open and functioning, is,

$\displaystyle\frac{1}{16}+ \displaystyle\frac{1}{12}=\displaystyle\frac{7}{48}$.

After two hours when tap A is closed, the portion of tank already filled up will be,

$\displaystyle\frac{14}{48}=\frac{7}{24}$.

Time take to fill up rest $\displaystyle\frac{17}{24}$ portion of the tank by B working alone will be,

$\displaystyle\frac{17}{24}\times{12}=8\displaystyle\frac{1}{2}$ hours.

#### Application of unitary method

1 portion of tank is filled up in 12 hours,

$\displaystyle\frac{17}{24}$ portion of tank will be filled up in, $\displaystyle\frac{17}{24}\times{12}$ hours.

**Answer:** Option d: $8\displaystyle\frac{1}{2}$.

**Key concepts used:** **Fill rate as portion of tank filled up in 1 hour -- Pipes working together -- Unitary method -- Solving in mind****.**

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

**Note:** even in such simple cases, apply unitary method to solve accurately.

**Q3. **When 25 men work for only 3 days, $\displaystyle\frac{4}{5}$th of the work remains unfinished. How much work will remain unfinished if 15 men work for only 4 days?

- $\displaystyle\frac{9}{10}$
- $\displaystyle\frac{11}{12}$
- $\displaystyle\frac{21}{25}$
- $\displaystyle\frac{13}{14}$
- $\displaystyle\frac{12}{13}$

**Solution 3: Problem analysis and solution by amount of work as mandays concept**

We will solve this problem mentally by applying the concept of mandays representing amount of work.

In $25\times{3}=75$ mandays effort $1-\displaystyle\frac{4}{5}=\displaystyle\frac{1}{5}$th of the work gets finished.

So the total work amount is $75\times{5}=375$ mandays.

Completion of $15\times{4}=60$ mandays work will then leave,

$\displaystyle\frac{375-60}{375}=\displaystyle\frac{315}{375}=\displaystyle\frac{21}{25}$ as unfinished portion of the total work (leftover work here is, 315 mandays which must be divided by the total work to get the unfinished portion of the total work).

**Answer:** Option c: $\displaystyle\frac{21}{25}$.

**Key concepts used: ***Work amount as mandays -- Leftover work -- Solving in mind***.**

**Note: **To accurately produce the answer, the unifinished mandays is to be divided by total mandays for evaluating the unifinished portion of total work. Mandays measure is only an intermediate measure of work to simplify solution.

The problem could easily be solved in mind.

**Q4. **P, Q and R each working alone can finish a job in 27, 33 and 45 days respectively. P starts working alone for 12 days, then Q takes over from P and work for 11 days. At this stage R takes over from Q and completes the remaining work. In how many days was the whole work completed?

- 33 days
- 35 days
- 37 days
- 39 days
- 31 days

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

From the given statement, portion of work done in a day by 12 days work of P followed by 11 days work of Q, is,

$\displaystyle\frac{12}{27}+\displaystyle\frac{11}{33}=\displaystyle\frac{4}{9}+\displaystyle\frac{1}{3}=\displaystyle\frac{7}{9}$

So leftover work, $\displaystyle\frac{2}{9}$ will be completed by R who completes whole work in 45 days, in a duration of,

$\displaystyle\frac{2}{9}\times{45}=10$ days, by work time direct proportionality.

Total work completion duration will thus be,

$12+11+10=33$ days.

**Answer:** Option a: 33 days.

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

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

**Q5. **A and B together can complete a given work in 9 days. Working alone A takes 24 days less than B working alone to complete the work. In how many days will B working alone complete the work?

- 36 days
- 45 days
- 54 days
- 42 days
- None of the above

**Solution 5: Problem solving using work rate as work portion done in a day **

Let's assume $d$ as the number of days taken by B working alone to complete the work.

So from the problem statement we have,

$\displaystyle\frac{1}{d-24}+\displaystyle\frac{1}{d}=\displaystyle\frac{1}{9}$

Or, $9(2d-24)=d^2-24d$,

Or, $d^2-42d+212=0$,

Or, $(d-36)(d-6)=0$.

As $d$ cannot be smaller than 24,

$d=36$.

**Answer:** Option a: 36 days.

*Key concepts used:* *Work rate as work portion done in a day*** -- Working together -- Solving quadratic equation.**

We wrote down only the quadratic equation to factorize by mid-term splitting comfortable.

**Q6.** A group of workers could complete a piece of work in 84 days. If there were 6 more workers, it would have taken 12 days less to finish the piece of work. What was the original strength of workers?

- 40
- 32
- 48
- 36
- 42

**Solution 6: Problem analysis and solution by mandays technique**

Using mandays technique as a measure of work amount, and assuming $n$ as the original number of workers we form the relation between total work amounts,

$84n=(n+6)(84-12)=72(n+6)$,

Or, $7n=6n+36$,

Or, $n=36$.

**Answer:** Option d : 36.

**Key concepts used:** ** Work amount as mandays -- Mandays technique -- Solving in mind**.

The problem was simple enough to solve mentally and quickly. Only, use of suitable technique was necessary.

**Q7.** 18 men can complete a piece of work in 24 days and 12 women can complete the same piece of work in 32 days. 18 men start working and after a few days, 4 men leave the job and 8 women join. If the remaining work was completed in $15\displaystyle\frac{15}{23}$ days, after how many days did the four men leave?

- 2 days
- 5 days
- 4 days
- 6 days
- 8 days

**Solution 7: Problem analysis and key pattern identification using work amount as mandays, and worker equivalence concepts**

On a brief analysis of the total work amount in mandays and womandays we identified a simple relationship between 1 manday and 1 womanday. This is the key pattern as, by this * worker equivalence* we would be able to substitute the group of women by an equivalent number of men thereby simplifying the evaluation greatly. Usually in this type of problem where groups of men and women complete a job in specific number of days, one must try for possibility of worker equivalence.

Let us explain the key pattern of simple relation between capacity of work of a man and a woman. This plays a key role in quick solution of the problem.

First we equate the total work amount as mandays and womandays,

$\text{Total work}=18\times{24}\text{ mandays}=12\times{32}\text{ womandays}$,

Or, $9\text{ mandays}=8\text{ womandays}$.

In other words, work done in a specific period by 9 men equals work done in the same period by 8 woman. This is worker equivalence.

In the final phase of the work, substituting 8 women by 9 men, effectively 23 men worked. This awkward number cancels out the denominator in the number of days. This is the second key pattern, and the concepts and techniques applied form the key strategy.

#### Solution 7: Problem solution by worker equivalence and work portion to work time direct proportionality

From the last fragment of statement, 14 men and 8 women work for $15\frac{15}{23}=\displaystyle\frac{360}{23}$ days, we can now substitute 8 women by 9 men. So effectively, a total of $14+9=23$ men work during this period and complete,

$\displaystyle\frac{360}{18\times{24}}=\frac{5}{6}$th of the work.

Rest $\displaystyle\frac{1}{6}$th of the work was then completed by 18 men earlier.

As same number of 18 men take 24 days to complete the whole work, to complete $\displaystyle\frac{1}{6}$th of the whole work,

$\displaystyle\frac{24}{6}=4$ days will be required.

**Answer:** Option c: 4 days.

** Key concepts used:** *Problem analysis -- Key pattern identification -- Work amount as mandays -- Worker equivalence -- Work time proportionality -- Mathematical reasoning -- Solving in mind.*

We try not to use any formula as it loads the memory. Instead, we use concepts, patterns and methods along with problem analysis that determines the strategies and methods that need to be applied most effectively.

The problem could be solved in mind in a few tens of seconds with a bit more attention than usual.

**Q8.** A work can be finished by 36 workers in 14 days. If the work were to be finished in 8 days, how many additional workers would be required?

- 29
- 31
- 23
- 33
- 27

** Solution 8: Problem analysis and solution by Mandays technique**

Total work amount is,

$36\times{14}$ mandays.

To finish this work in 8 days total number of men required will be,

$\displaystyle\frac{36\times{14}}{8}=63$.

So an additional number of, $63-36=27$ men will be required to finish the work in 8 days.

**Answer:** Option e: 27.

**Key concepts used:** **Work amount as mandays -- Worker to work time inverse proportionality -- Solving in mind.**

**Q9.** A alone can finish a work in 42 days. B is 20% more efficient than A and C is 40% more efficient than B. In how many days B and C working together can finish the same piece of work?

- $12\displaystyle\frac{11}{12}$ days
- $11\displaystyle\frac{5}{12}$ days
- $15\displaystyle\frac{1}{12}$ days
- $14\displaystyle\frac{7}{12}$ days
- $13\displaystyle\frac{5}{12}$ days

**Solution 9: Problem analysis and solution by worker equivalence concept**

By the given condition, B is equivalent to 1.2 of A (converting percentage to decimal).

Similarly C will be equivalent to $1.4\text{ of B}=1.4\times{1.2}\text{ of A}$.

So when B and C work together, effectively they will be equivalent to, $1.2+1.4\times{1.2}=1.2\times{2.4}\text{ of A}$ working.

Using unitary method on inverse relation between worker and time to complete,

1 of A completes the work in 42 days,

So $1.2\times{2.4}$ of A will complete the work in,

$\displaystyle\frac{42}{1.2\times{2.4}}=\frac{7}{0.48}$

$=\displaystyle\frac{700}{48}$

$=\displaystyle\frac{175}{12}$

$=14\displaystyle\frac{7}{12}$ days.

**Answer:** Option d: $14\displaystyle\frac{7}{12}$ days.

**Key concepts used:** * Worker equivalence concept -- Worker efficiency concept -- Percentage to decimal conversion* --

*--*

**Worker to time inverse proportionality**

**Unitary method on inverse proportionality -- Solving in mind.**The problem could be solved in mind primarily because of converting worker efficiency to worker equivalence and use of percentage to decimal conversion.

**Q10.** Two pipes can fill a tank in 12 hrs and 16 hrs respectively. A third pipe can empty the tank in 30 hrs. If all the three pipes were opened and function simultaneously, in how many hrs would the tank be full?

- $10\displaystyle\frac{4}{9}$ hrs
- $7\displaystyle\frac{2}{9}$ hrs
- $9\displaystyle\frac{1}{9}$ hrs
- $9\displaystyle\frac{5}{9}$ hrs
- $8\displaystyle\frac{8}{9}$ hrs

**Solution 10: Problem analysis and solution by fill rate and working together concepts**

Adding the fill rates for the two filling pipes and subtracting the emptying rate of the emptying pipe we get the portion of tank effectively filled in 1 hr when all three pipes work together as,

$\displaystyle\frac{1}{12}+\displaystyle\frac{1}{16}-\displaystyle\frac{1}{30}$

$=\displaystyle\frac{20+15-8}{240}$

$=\displaystyle\frac{27}{240}$

$=\displaystyle\frac{9}{80}$.

Inverting, the number of hrs required to fill the tank is,

$\displaystyle\frac{80}{9}=8\displaystyle\frac{8}{9}$ hrs.

**Answer: **Option e: $8\displaystyle\frac{8}{9}$ hrs.

**Key concepts used:** **Fill rate -- Emptying rate -- Solving in mind.**

The problem was simple enough to be comfortably and quickly solved in mind.

### 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*.