# Time and Work Practice Set 2

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# Time and Work Practice Set 2

### Introduction

Work is defined as the amount of job assigned or the amount of job actually done. Work is always considered as a whole or 1. Work based problems are more or less related to time speed and distance. The article Time and Work Practice Set 2 provides information about Time and Work, a important topic of Quantitative Aptitude section. Consists of different types questions with solutions useful for candidates preparing for different competitive examinations like RRB ALP/Technical Exams/Junior Engineer Recruitment Exams, SSC, IBPS PO Exams and etc.

### Quiz

1. A and B together can complete a particular task in 4 days. If A alone can complete the same task in 12 days. How many days will B take to complete the task if he works alone?

A. 9 days
B. 7 days
C. 5 days
D. 6 days

Explanation: A and B together finish a piece of work = x = 4 days

A alone finish a piece of work = y = 12 days.

By the short trick approach:

B alone can do the whole work in $$\frac{4 × 12}{12 – 4}$$
= $$\frac{40}{4}$$ = 6 days

2. 6 women can complete a piece of work in 10 days, whereas 10 children alone take 15 days to complete the same piece of work. How many days will 6 women and 10 children together take to complete the piece of work?

A. 7
B. 8
C. 6
D. 4

Explanation:
6 Women’s 1 day’s work = $$\frac{1}{10}$$;
10 Children’s 1 day’s work = $$\frac{1}{15}$$;
(6 women + 10 children)’s 1 day’s work = $$\frac{1}{10}$$ + $$\frac{1}{15}$$
= $$\frac{5}{30}$$
= $$\frac{1}{6}$$
So, total time taken to complete work = 16 + 6= 22 hrs.

3. Salim taken 8 days to finish a piece of work. Manoj takes 12 days to finish the same piece of work. Raj works twice as fast as Salim. How many days will all three of them together take to finish the same piece of work?

A. 2$$\frac{3}{11}$$
B. 3$$\frac{8}{13}$$
C. 3$$\frac{9}{13}$$
D. 2$$\frac{2}{11}$$

Explanation: Time taken by Salim = x = 8 days

Time taken by Manoj = y = 12 days

Time taken by Raj (Twice as fast as Salim) = z = 8/2 = 4 days

By the short trick approach:

A, B and C can do the work in $$\frac{8 × 12 × 4}{8 × 12 + 12 × 4 + 4 × 8}$$ $$\frac{×yz}{xy+yz+ zx }$$
After taking 8 as a common term we get,
$$\frac{48}{12 + 6 + 4}$$
= $$\frac{48}{22}$$
= $$\frac{24}{11}$$
= 2$$\frac{2}{11}$$days

4. A and B together can finish a work in 9 days. A alone can finish the work in 12 days. In how many days will B alone finish the work?

A. 24
B. 28
C. 32
D. 36

Explanation: Time taken by A and B together to finish a piece of work = x = 9 days

Time taken by A alone to finish the same piece of work = y = 12 days.

By the short trick approach:($$\frac{xy}{x – y}$$)

B alone can do the whole work in $$\frac{12 × 9}{12 – 9}$$ = $$\frac{108}{3}$$ = 36 days

5. P can finish a work in 25 days and Q can do the same work in 20 days. Q worked for 8 days and left the job. In how many days, P alone can finish the remaining work?

A. 5 days
B. 10 days
C. 15 days
D. 17 days

Explanation: Q’s 8 days work =[ $$\frac{1}{20}$$ x 8] work ⇒ $$\frac{2}{5}$$
Remaining work = [1 –$$\frac{2}{5}$$]
Now, $$\frac{1}{25}$$ work is done by P in 1 day
∴ $$\frac{3}{5}$$ work is done by P in [25 x $$\frac{3}{5}$$]

1. Nitin and Nirdosh together can complete a piece of work in 6 days. If Nitin alone can complete the same work in 24 days; in how many days can Nirdosh alone complete that work?

A. 8
B. 12
C. 14
D. 15

Explanation:
(Nitin + Nirdosh)’s 1 day’s work = $$\frac{1}{6}$$
Nitin’s 1 day’s work = $$\frac{1}{24}$$
∴ Nirdosh’s 1 day’s work $$\frac{1}{6}$$ – $$\frac{1}{24}$$⇒ $$\frac{3}{24}$$
⇒ $$\frac{1}{8}$$

2. A, B and C together earn Rs. 300 per day, while A and C together earn Rs. 188 and B and C together earn Rs. 152. The daily earning of C is:

A. Rs. 40
B. Rs. 68
C. Rs. 112
D. Rs. 150

Explanation: B’s daily earning = Rs. (300 – 188) = Rs. 112.

A’s daily earning = Rs. (300 – 152) = Rs. 148.

C’s daily earning = Rs. [300 – (112 + 148)] = Rs. 40

3. 10 men and 15 women together can complete a work in 6 days. It takes 100 days for one man alone to complete the same work. How many days will be required for one woman alone to complete the same work?

A. 125
B. 150
C. 200
D. 225

Explanation: 1 man’s 1 day’s work
$$\frac{1}{100}$$ , (10 men + 15 women)’s 1 day’s work = $$\frac{1}{6}$$
15 women’s 1 day’s work [$$\frac{1}{6}$$ – $$\frac{10}{100}$$] = [$$\frac{1}{6}$$ – $$\frac{1}{10}$$] = $$\frac{1}{15}$$

∴ 1 woman’s 1 day’s work = $$\frac{1}{125}$$
Then, 1 woman alone can complete the work in 225 days.

4. A girl can do a job in 10 days, Her mother takes 25 days and her sister finishes it in 20 days. How long will they take to complete the job if they all together?

A. Less than 5 days
B. Exactly 5 days
C. Approximately 5.3 days
D. 3$$\frac{5}{11}$$ hours
E. More than 6 days

Explanation: 1 day’s work of the three persons

= [$$\frac{1}{10}$$ +$$\frac{1}{25}$$+$$\frac{1}{20}$$ ] ⇒
($$\frac{10 + 4 + 5 }{100}$$)= $$\frac{19}{100}$$
Hence, the printing of books will be completed at 5($$\frac{1}{11}$$)hours
So all the three together will complete the work in $$\frac{100}{19}$$ = 5.3 days

5. A and B together can complete a piece of work in 12 days, B and C can do it in 20 days and C and A can do it in 15 days. A, B and C together can complete it in

A. 12 days
B. 6 days
C. 8 days
D. 10 days

Explanation: If A and B can do a piece of work in x days, B and C in y days, C and A in z days, then (A + B + C) working together will do the same work in
$$\frac{2xyz}{xy + yz + zx}$$
A and B together finish a piece work = x = 12 days

B and C together finish a piece work = y = 20 days

C and A together finish a piece work = z = 15 days

By the short trick approach:

A, B and C can do the work in $$\frac{2 × 12 × 20 × 15}{12 × 20 + 20 × 15 + 15 × 12}$$ days
After taking 20 as a common term we get, = $$\frac{2 × 12 × 15}{12 + 15 + 9}$$ days
After taking 3 as a common term we get, $$\frac{2 × 14 × 15}{4 + 5 + 3}$$ days = $$\frac{120}{ 12}$$ = 10 days

1. A works alone, he would take 4 days more to complete the job than if both A and B worked together. If B worked alone, he would take 16 days more to complete the job than if both A and B work together. How many days would they take to complete the work if both of them worked together?

A. 10 days
B. 12 days
C. 6 days
D. 8 days

Explanation:
To solve this question, we can apply a short trick approach;

If A working alone takes ‘x’ days more than A and B, and B working alone takes ‘y’ days more than

A & B together then the number of days taken by A & B working together is given by $$\sqrt{xy}$$ days.
A’s time = x = 4 days
B’s time = y = 16 days

By the short trick approach:$$\sqrt{4 × 16}$$ = $$\sqrt{64}$$ = 8 days

2. ‘A’ can do a piece of work in 20 days and ‘B’ can do the same work in 15 days. How long will they take to finish the work, if both work together?

A. 15 days
B. 10 days

C. 8 × $$\frac{4}{7}$$ days
D. 20 days

Explanation: A’s time = x = 20 days

B’s time = y = 15 days

By the short trick approach:
A + B can do the work in

8 × $$\frac{20 × 15}{20 + 15}$$ days = $$\frac{300}{35}$$ = $$\frac{60}{7}$$ = 8 × $$\frac{4}{7}$$ days

3. Ashokan is thrice as good a workman as Nitin and is therefore able to finish a piece of work in 40 days less than Nitin. Find the time in which they can do it working together.

A. 15 days
B. 7 days
C. 16 days
D. 13 days

Explanation:If A is ‘n’ times as fast (or slow) as B, and is therefore able to finish a work in ‘D’ days less (or more) than B, then the time in which they can do it working together is given by

Therefore, x = ($$\frac{Dn}{{n}^{2} – 1}$$)
Ashokan’s days less then Nitin = D = 40 days

Ashokan is 3 times as fast as Nitin = n = 3.

By the short trick approach:

we have the Required answer $$\frac{40 × 3}{{3}^{2} – 1}$$
= $$\frac{40 × 3}{8}$$ = 15 days

4. A completes a piece of work in 4 days and B completes it in 6 days. If they both work on it together, then the number of days required to complete the same work is

A. 3$$\frac{5}{2}$$ days
B. 2$$\frac{3}{5}$$ days
C. 2$$\frac{2}{5}$$ days
D. 3$$\frac{2}{5}$$ days

Explanation:A’s time = x = 4 days

B’s time = y = 6 days

By short trick approach:

A + B can do the work in = $$\frac{4 × 6}{4 + 6}$$days

$$\frac{24}{10}$$ = 2$$\frac{2}{5}$$ days

5. A is twice as good a workman as B and together they finish a piece of work in 14 days. The number of days taken by A alone to finish the work is

A. 11 days
B. 21 days
C. 28 days
D. 42 days

Explanation: By the short trick approach:

A finish the work in $$\frac{2 + 1}{2}$$× 14 = 21 days [$$\frac{n + 1}{2}$$ x (n + 1)x ]

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