# Time and Work – Quiz 2

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# Time and Work – Quiz 2

### Introduction

Time and Work is one of important topic in Quantitative Aptitude Section. In Time and Work – Quiz 2 article candidates can find a question with an answer. By solving this question candidates can improve and maintain, speed, and accuracy in the exams. Time and Work - Quiz 2 questions are very useful for different exams such as IBPS PO, Clerk, SSC CGL, SBI PO, NIACL Assistant, NICL AO, IBPS SO, RRB, Railways, UPSC, IES and Civil Services etc.

### Q1

A can do a piece of work in 4 hours; B and C together can do it in 3 hours, while A and C together can do it in 2 hours. How long will B alone take to do it?
A. 8 hours B. 10 hours C. 12 hours D. 24 hours

C
A's 1 hour's work = $\frac{1}{4}$;
(B + C)'s 1 hour's work = $\frac{1}{3}$;
(A + C)'s 1 hour's work = $\frac{1}{2}$;
(A + B + C)'s 1 hour's work = $(\frac{1}{4} + \frac{1}{3}) = \frac{7}{12}$.
B's 1 hour's work = $(\frac{7}{12} - \frac{1}{2}) = \frac{1}{12}$.
i.e, B alone will take 12 hours to do the work.

### Q2

A can do a certain work in the same time in which B and C together can do it. If A and B together could do it in 10 days and C alone in 50 days, then B alone could do it in:
A. 15 days B. 25 days C. 20 days D. 30 days

B
(A + B)'s 1 day's work = $\frac{1}{10}$
C's 1 day's work = $\frac{1}{50}$
(A + B + C)'s 1 day's work = $(\frac{1}{10} + \frac{1}{50}) = \frac{6}{50} = \frac{3}{25}$............(i)
A's 1 day's work = (B + C)'s 1 day's work .... (ii)
From (i) and (ii), we get: 2 x (A's 1 day's work) = $\frac{3}{25}$
$\Rightarrow$ A's 1 day's work = $\frac{3}{50}$
i.e, B's 1 day's work $(\frac{1}{10} - \frac{3}{50}) = \frac{2}{50} = \frac{1}{25}$
So, B alone could do the work in 25 days.

### Q3

A does 80% of a work in 20 days. He then calls in B and they together finish the remaining work in 3 days. How long B alone would take to do the whole work?
A. 23 days B. 37 days C. 37 $\frac{1}{2}$ days D. 40 days

C
Whole work is done by A in
$(20 \times \frac{5}{4})$ = 25 days.
Now, $(1 - \frac{4}{5})$ i.e, $\frac{1}{5}$ work is done by A and B in 3 days.
Whole work will be done by A and B in (3 x 5) = 15 days.
i.e, B's 1 day's work = $(\frac{1}{15} - \frac{1}{25}) = \frac{4}{150} = \frac{2}{75}$
So, B alone would do the work in $\frac{75}{2} = 37 \frac{1}{2}$ days

### Q4

A can finish a work in 18 days and B can do the same work in 15 days. B worked for 10 days and left the job. In how many days, A alone can finish the remaining work?
A. 5 days B. 5 $\frac{1}{2}$ days C. 6 days D. 8 days

C
B's 10 day's work = $(\frac{1}{15}\times 10) = \frac{2}{3}$
Remaining work = $(1 - \frac{2}{3}) = \frac{1}{3}$
Now, $\frac{1}{18}$ work is done by A in 1 day.
i.e, $\frac{1}{3}$ work is done by A in $(\frac{1}{3}\times 18)$ = 6 days

### Q5

4 men and 6 women can complete a work in 8 days, while 3 men and 7 women can complete it in 10 days. In how many days will 10 women complete it?
A. 35 days B. 40 days C. 45 days D. 50 days

B
Let 1 man's 1 day's work = x and 1 woman's 1 day's work = y.
Then, 4x + 6y = $\frac{1}{8}$, and 3x + 7y = $\frac{1}{10}$
Solving the two equations, we get: x = $\frac{11}{400}$, y = $\frac{1}{400}$
i.e, 1 woman's 1 day's work = $\frac{1}{400}$
$\Rightarrow$ 10 women's 1 day's work = $(\frac{1}{400} \times 10) = \frac{1}{40}$
Hence, 10 women will complete the work in 40 days.