## 1st set of 10 solved SSC CHSL time and work questions

This is the 1st set of 10 solved SSC CHSL time and work questions to be used as a mini mock test practice. It contains,

- 1st
**set of 10 carefully selected questions on Time and work**for SSC CHSL to be answered in 15 minutes. **Answers**to the questions, and- Detailed
**conceptual solutions**to the questions.

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 set of 10 SSC CHSL time and work questions: Answering time 15 mins

**Q1. **A takes 10 days less than B to finish a job. If both of them work together, they can finish the job in 12 days. In how many days would B be able to finish the same job while working alone?

- 27 days
- 25 days
- 20 days
- 30 days

**Q2.** A can do a work in 21 days. B is 40% more efficient than A. The number of days required for B to finish the same work is,

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

**Q3. **P is thrice as good a workman as Q and therefore he is able to finish a job in 48 days less than Q. Working together, they would be able to finish the job then in,

- 30 days
- 18 days
- 24 days
- 12 days

**Q4. **39 persons can repair a road in 12 days working 5 hours a day. In how many days will 30 persons working 6 hours a day complete the work?

- 13 days
- 10 days
- 14 days
- 15 days

**Q5. **Some carpenters promised to do a job in 9 days, but 5 of them were absent and remaining men did the job in 12 days. The original number of carpenters were,

- 18
- 16
- 20
- 24

**Q6.** A alone can do a piece of work in 20 days and B alone in 30 days. They begin to work together. They will finish half the work in,

- 8 days
- 9 days
- 12 days
- 6 days

**Q7.** A can do $\displaystyle\frac{1}{6}$th of a work in 5 days and B can do $\displaystyle\frac{2}{5}$th of the work in 8 days. In how many days would A and B working together complete the work?

- 12 days
- 15 days
- 20 days
- 13 days

**Q8.** If 1 man or 2 women or 3 boys can complete a work in 88 days, then 1 man, 1 woman and 1 boy together will complete it in,

- 36 days
- 42 days
- 54 days
- 48 days

**Q9.** If 4 men or 6 women can do a job in 12 days working 7 hours a day, how many days will it take to complete a work twice as large with 10 men and 3 women working together 8 hours a day?

- 6 days
- 8 days
- 7 days
- 10 days

**Q10.** 45 men can complete a work in 16 days. Four days after they started working, 36 more men joined them. How many days will they now take to complete the work?

- $6\displaystyle\frac{2}{3}$ days
- $7\displaystyle\frac{3}{4}$ days
- $8$ days
- $6$ days

### Answers to the questions

Q1. Answer: Option d: 30 days.

Q2. Answer: Option c : 15 days.

Q3. Answer: Option b: 18 days.

Q4. Answer: Option a: 13 days.

Q5. Answer: Option c: 20.

Q6. Answer: Option d : 6 days.

Q7. Answer: Option a: 12 days.

Q8. Answer: Option d: 48 days.

Q9. Answer: Option c: 7 days.

Q10. Answer: Option a: $6\displaystyle\frac{2}{3}$ days.

### Solutions to the 1st set of 10 SSC CHSL time and work questions: Answering time was 15 mins

**Q1. **A takes 10 days less than B to finish a job. If both of them work together, they can finish the job in 12 days. In how many days would B be able to finish the same job while working alone?

- 27 days
- 25 days
- 20 days
- 30 days

** Solution 1: Problem analysis**

We would assume $x$ as the number of days taken for B to finish the job alone, because that is the desired quantity. So A will complete the job in $(x-10)$ days.

By **working together concept**, we get the portion of job done by A and B working together in a day by adding portions of job done by each of them in a day. These are their work rates.

This is the basic concept on which the solution depends.

As A completes the job in $(x-10)$ days, he does $\displaystyle\frac{1}{x-10}$ portion of whole work in 1 day working alone.

Similarly B does $\displaystyle\frac{1}{x}$ portion of whole work in a day working alone.

Adding the two we would get the portion of job done by both working together in 1 day from which value of $x$ is to be solved.

#### Solution 1: Problem solving execution

For precision of expressing situations we would assume $W$ as the quantum of work.

So work done by A and B together in a day is,

$\displaystyle\frac{W}{x-10}+\displaystyle\frac{W}{x}=\displaystyle\frac{W}{12}$, in 12 days together they finish work $W$, so in 1 day they do work, $\displaystyle\frac{W}{12}$.

Eliminating $W$,

$\displaystyle\frac{1}{x-10}+\displaystyle\frac{1}{x}=\displaystyle\frac{1}{12}$

#### Quick solution 1

Comparing the denominators on the RHS and LHS we can conclude, $x$ must be an even number. We have used **basic factors and multiples concept**. As 12 has a factor of 2, the LHS denominator must also have a factor of 2. As LCM of LHS denominator is $x(x-10)=x^2 - 10x$, $x$ must be even for the LHS denominator to be even.

Examining the choice values, we find two even choices, 20 and 30. Putting 20 as $x$ doesn't produce the RHS while $x=30$ produces the RHS value perfectly.

**Answer:** Option d: 30 days.

**Key concepts used:** * Basic factors multiples concept* --

*--*

**Work time concept***--*

**Work rate concept***--*

**Working together concept***--*

**Choice value test***.*

**Free resource use principle**#### Conventional solution 1

Otherwise, you can form the quadratic equation in single variable $x$,

$\displaystyle\frac{1}{x-10}+\displaystyle\frac{1}{x}=\displaystyle\frac{1}{12}$,

Or, $x^2 - 34x + 120=0$.

This we solve by middle term splitting method. Just by educated guess or trial, we decide that, $34=30+4$, would create the two factors,

$(x-30)(x-4)=0$.

$x$ cannot be 4 because $x-10$ would then be negative.

So $x=30$.

This is a mathematical conventional solution and takes more time.

**Q2.** A can do a work in 21 days. B is 40% more efficient than A. The number of days required for B to finish the same work is,

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

**Solution 2: Use of basic and rich work time concepts**

Assuming $W_A$ and $W_B$, the work portion done per day by A and B respectively, as B is 40% more efficient workman than A,

$W_B=1.4W_A$, 40% is equivalent to 0.4 and 100% to 1, adding we get 1.4 times.

As A can do the work in 21 days,

$21W_A=W$, $W$ is the total amount of work,

Or, $\displaystyle\frac{21}{1.4}W_B=W$,

Or, $15W_B=W$.

B does the work alone in 15 days.

**Answer:** Option c : 15 days.

**Key concepts used:** **Work rate concept -- Work rate comparison concept -- Percentage concept****.**

As *time required to complete the work is inversely proportional to work rate*, the result tallies with the problem statement. 40% of 15 days is 6 days. So B working 40% faster than A, days taken by A will be 40% more than B, that is $15+6=21$ days.

**Q3. **P is thrice as good a workman as Q and therefore he is able to finish a job in 48 days less than Q. Working together, they would be able to finish the job then in,

- 30 days
- 18 days
- 24 days
- 12 days

**Solution 3: Problem analysis and execution**

P, working three times faster than Q, finishes the work in 48 days less than Q. So 48 days must be $\displaystyle\frac{2}{3}$rd of the time taken by Q to finish the work, which turns out to be 72.

This is because time taken to finish the work is inversely proportional to the speed of work. So P will take take $\displaystyle\frac{1}{3}$rd of what Q will take. The difference of their days of completion will be $\displaystyle\frac{2}{3}$rd of days Q will take, which is 48 days. This is mathematical reasoning based on inverse relationship of days and speed, as well as change analysis technique.

The days Q will take then to finish the work is $\displaystyle\frac{3}{2}$ of 48, that is 72 days, and P will take 24 days.

So in 1 day working together they will finish portion of work as sum of their individual work rates per day,

$\displaystyle\frac{1}{24}+\displaystyle\frac{1}{72}$

$=\displaystyle\frac{1}{24}\left(1+\displaystyle\frac{1}{3}\right)$

$=\displaystyle\frac{1}{24}\times{\displaystyle\frac{4}{3}}$

$=\displaystyle\frac{1}{18}$.

So together P and Q will take 18 days to complete the work.

**Answer:** Option b: 18 days.

**Key concepts used: Work time Work rate inverse proportionality -- Work rate comparison -- Change analysis -- Working together **

**.**

**Q4. **39 persons can repair a road in 12 days working 5 hours a day. In how many days will 30 persons working 6 hours a day complete the work?

- 13 days
- 10 days
- 14 days
- 15 days

**Solution 4 - Problem analysis and execution**

We will use in this case mandays concept in general which translates to manhours measure of work amount for this problem, as the smallest time unit is hour here.

Total amount of work,

$W=39\times{12}\times{5}$ man hours

If number of days required is $d$, for the desired second case, work amount,

$W=39\times{12}\times{5}=30\times{d}\times{6}$

Or, $d=\displaystyle\frac{39\times{10}}{30}=13$

**Answer:** Option a: 13 days.

**Key concepts used: mandays concept -- manhours as a measure of work amount****.**

**Q5. **Some carpenters promised to do a job in 9 days, but 5 of them were absent and remaining men did the job in 12 days. The original number of carpenters were,

- 18
- 16
- 20
- 24

**Solution 5 - Problem analysis and execution using mandays concept**

Assuming $x$ number of men were there in the original team, this team to complete the work in 9 days, the amount of work would be $9x$ mandays.

Same work is completed by $(x-5)$ number of men in 12 days doing work amount of $12(x-5)$ mandays.

Equating the two,

$12(x-5)=9x$,

Or $3x=60$,

Or $x=20$

In original team there were 20 men.

**Answer:** Option c: 20.

*Key concepts used:* **Mandays concept****.**

**Q6.** A alone can do a piece of work in 20 days and B alone in 30 days. They begin to work together. They will finish half the work in,

- 8 days
- 9 days
- 12 days
- 6 days

**Solution 6 - Problem analysis and execution**

Adding the per day work rates of A and B we get the per day work portion done by the two working together as,

$\displaystyle\frac{1}{20}+\displaystyle\frac{1}{30}=\displaystyle\frac{1}{12}$

So A and B working together will take 12 days to complete the whole job, and 6 days to complete the half of the job.

**Answer:** Option d : 6 days.

**Key concepts used:** ** Working together concept -- work portion done by the workers working together in a day is sum of work portion done by each in a day**.

** Q7.** A can do $\displaystyle\frac{1}{6}$th of a work in 5 days and B can do $\displaystyle\frac{2}{5}$th of the work in 8 days. In how many days would A and B working together complete the work?

- 12 days
- 15 days
- 20 days
- 13 days

**Solution 7 - Problem analysis and excution -- working together and work rate concept**

A does $\displaystyle\frac{1}{6}$th of a work in 5 days. So his work rate in terms of work portion done in a day is,

$\displaystyle\frac{1}{30}$, work done is directly proportional to number of days work done at same work rate.

B does $\displaystyle\frac{2}{5}$th of the same work in 8 days. So his work rate in terms of work portion done in a day is,

$\displaystyle\frac{1}{20}$.

Adding the two we get work portion done in a day when A and B work together as,

$\displaystyle\frac{1}{30}+\displaystyle\frac{1}{20}$

$=\displaystyle\frac{1}{12}$.

They will take 12 days to complete the work when working together.

**Answer:** Option a: 12 days.

** Key concepts used:** ** Work rate of each worker in terms of work portion done in a day **--

**Working together concept, work portion done by workers working together is sum of their work rates.**** Q8.** If 1 man or 2 women or 3 boys can complete a work in 88 days, then 1 man, 1 woman and 1 boy together will complete it in,

- 36 days
- 42 days
- 54 days
- 48 days

** Solution 8 - Problem analysis and execution**

As same work is done in same number of days by 1 man or 2 women separately, work rate of 1 woman is $\displaystyle\frac{1}{2}$ of work rate of a man which is $\displaystyle\frac{1}{88}$.

Similarly, work rate of a boy is $\displaystyle\frac{1}{3}$ rd of that of a man.

So when 1 man, 1 woman and 1 boy work together, work portion done in a day by them is,

$\displaystyle\frac{1}{88}\left(1+\displaystyle\frac{1}{2}+\displaystyle\frac{1}{3}\right)$

$=\displaystyle\frac{1}{88}\times{\displaystyle\frac{11}{6}}$

$=\displaystyle\frac{1}{48}$.

Together they will then complete the work in 48 days.

**Answer:** Option d: 48 days.

**Key concepts used:** * Work equivalence of workers* --

*--*

**Work rate in terms of work portion done by a worker in a day**

**When Working together, work portion done by the workers as sum of individual work rates**

**-- Efficient simplification.**We have not multiplied 88 and kept it separately as a common factor for ease of simplification. This is efficient simplification.

**Q9.** If 4 men or 6 women can do a job in 12 days working 7 hours a day, how many days will it take to complete a work twice as large with 10 men and 3 women working together 8 hours a day?

- 6 days
- 8 days
- 7 days
- 10 days

**Solution 9 - Problem analysis and execution -- worker equivalence concept -- mandays concept**

4 men do the job of 6 women. So by Worker equivalence concept, work of 2 men is equivalent to work of 3 women.

In the first case, work $W$ is done by 4 men in 12 days working 7 hours a day. So work amount in terms of manhours is,

$W=4\times{12}\times{7}$ manhours.

Using delayed evaluation technique we don't calculate the result at this point of time.

In the next stage twice as large as the first time work, that is, $2W$ work is done by 10 men and 3 women in say, $d$ number of days. As 3 women work is equivalent to 2 men work, effectively in second case 12 men work. So,

$12\times{d}\times{8}=2W=2\times{4}\times{12}\times{7}$

So,

$d=7$.

**Answer:** Option c: 7 days.

**Key concepts used:** * Worker equivalence -- mandays concept* --

**Efficient simplification.**** Q10.** 45 men can complete a work in 16 days. Four days after they started working, 36 more men joined them. How many days will they now take to complete the work?

- $6\displaystyle\frac{2}{3}$ days
- $7\displaystyle\frac{3}{4}$ days
- $8$ days
- $6$ days

**Solution 10 - Problem analysis and execution**

In 16 days 45 men finish the work $W$. So in 4 days they work they will finish $\displaystyle\frac{1}{4}$th of the work with $\displaystyle\frac{3}{4}$th of the work remaining.

So the remaining work in terms of mandays will be,

$\displaystyle\frac{3}{4}W=\displaystyle\frac{3}{4}\times{45\times{16}}=45\times{12}$ mandays

This work will be done say, in $d$ number of days by $45+36=81$ men. So,

$81d=45\times{12}$,

Or, $d=\displaystyle\frac{20}{3}=6\displaystyle\frac{2}{3}$ days

So the remaining work will be done in $6\displaystyle\frac{2}{3}$ days

**Answer: **Option a: $6\displaystyle\frac{2}{3}$ days.

Instead of going into any other complications, we have just used the proportion of job in terms of mandays of work remaining. That's the advantage of having a measure of the job in concrete numeric terms. Mandays provides this.

**Key concepts used:** **Mandays concept -- Proportion concept -- efficient simplification.**

The problem could be solved in mind in quicktime.

### Useful resources to refer to

#### Guidelines, Tutorials and Quick methods to solve Work Time problems

**7 steps for sure success in SSC CGL Tier 1 and Tier 2 competitive tests**

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