# Time and Work – Quiz 1

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# Time and Work – Quiz 1

### Introduction

Time and Work is one of important topic in Quantitative Aptitude Section. In Time and Work – Quiz 1 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 1 questions are very useful for different exams such as IBPS PO, Clerk, SSC CGL, SBI PO, NIACL Assistant, NICL AO, IBPS SO, RRB, Railways, Civil Services etc.

### Q1

A can do a work in 15 days and B in 20 days. If they work on it together for 4 days, then the fraction of the work that is left is :
A. $\frac{1}{4}$ B. $\frac{1}{10}$ C. $\frac{7}{15}$ D. $\frac{8}{15}$

D
A's 1 day's work = $\frac{1}{15}$
B's 1 day's work = $\frac{1}{20}$
(A + B)'s 1 day's work = $( \frac{1}{15} +\frac{1}{20}) = \frac{7}{60}$
(A + B)'s 4 day's work = $( \frac{7}{60} \times 4) = \frac{7}{15}$
Therefore, Remaining work =$(1 - \frac{7}{15}) = \frac{8}{15}$

### Q2

A can lay railway track between two given stations in 16 days and B can do the same job in 12 days. With help of C, they did the job in 4 days only. Then, C alone can do the job in:
A. $9 \frac{1}{5}$ B. $9 \frac{2}{5}$ C. $9 \frac{3}{5}$ D. 10

C
(A + B + C)'s 1 day's work = $\frac{1}{4}$,
A's 1 day's work = $\frac{1}{16}$,
B's 1 day's work = $\frac{1}{12}$
Therefore C's 1 day's work = $\frac{1}{4} - (\frac{1}{16} + \frac{1}{12}) = (\frac{1}{4} + \frac{7}{48})= \frac{5}{48}$
So, C alone can do the work in $\frac{48}{5} = 9 \frac{3}{5}$days.

### Q3

A, B and C can do a piece of work in 20, 30 and 60 days respectively. In how many days can A do the work if he is assisted by B and C on every third day?
A. 12 days B. 15 days C. 16 days D. 18 days

B
A's 2 day's work = $(\frac{1}{20} \times 2) = \frac{1}{10}$
(A + B + C)'s 1 day's work = $(\frac{1}{20} + \frac{1}{30} + \frac{1}{60}) = \frac{6}{60} = \frac{1}{10}$
Work done in 3 days = $(\frac{1}{10} + \frac{1}{10}) = \frac{1}{5}$
Now, $\frac{1}{5}$ work is done in 3 days.
i.e, Whole work will be done in (3 x 5) = 15 days.

### Q4

A is thrice as good as workman as B and therefore is able to finish a job in 60 days less than B. Working together, they can do it in:
A. 20 days B. 22 $\frac{1}{2}$ days C. 25 days D. 30 days

B
Ratio of times taken by A and B = 1 : 3.
The time difference is (3 - 1) 2 days while B take 3 days and A takes 1 day.
If difference of time is 2 days, B takes 3 days.
If difference of time is 60 days, B takes $(60 \times \frac{3}{2})$ = 90 days.
So, A takes 30 days to do the work.
A's 1 day's work = $\frac{1}{30}$
B's 1 day's work = $\frac{1}{90}$
(A + B)'s 1 day's work = $(\frac{1}{30} + \frac{1}{90}) = \frac{4}{90} = \frac{2}{45}$
i.e, A and B together can do the work in $\frac{2}{45} = 22 \frac{1}{2}$

### Q5

A alone can do a piece of work in 6 days and B alone in 8 days. A and B undertook to do it for Rs. 3200. With the help of C, they completed the work in 3 days. How much is to be paid to C?
A. Rs. 375 B. Rs. 600 C. Rs. 400 D. Rs. 800

C
C's 1 day's work = $\frac{1}{3} - (\frac{1}{6} + \frac{1}{8}) = \frac{1}{3} - \frac{7}{24} = \frac{1}{24}$
A's wages : B's wages : C's wages = $\frac{1}{6} : (\frac{1}{6} + \frac{1}{8}) : \frac{1}{24}= 4 : 3 : 1$
i.e, C's share (for 3 days) = Rs. $(3 \times \frac{1}{24} \times) = Rs. 400.$