# Time and Work – Quiz 5

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# Time and Work – Quiz 5

### Introduction

Time and Work is one of important topic in Quantitative Aptitude Section. In Time and Work – Quiz 5 article candidates can find questions with an answer. By solving this questions candidates can improve and maintain, speed, and accuracy in the exams. Time and Work – Quiz 5 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 finish a work in 24 days, B in 9 days and C in 12 days. B and C start the work but are forced to leave after 3 days. The remaining work was done by A in:
A. 5 days B. 6 days C. 10 days D. 20 days

C
(B + C)'s 1 day's work = ($\frac {1}{9}$ + $\frac {1}{12}$) = $\frac {7}{36}$
Work done by B and C in 3 days = ($\frac {7}{36} \times 3$) = $\frac {7}{12}$
Remaining work = (1- $\frac {7}{12}$) = $\frac {5}{12}$
Now, $\frac {1}{24}$ work is done by A in 1 day.
So, $\frac {7}{12}$ work is done by A in ($24 \times \frac {5}{12}$) = 10 days

### Q2

X can do a piece of work in 40 days. He works at it for 8 days and then Y finished it in 16 days. How long will they together take to complete the work?
A. 13 1/3 days B. 15 days C. 20 days D. 26 days

A
Work done by X in 8 days = ($\frac{1}{40}$ x 8) = $\frac{1}{5}$
Remaining work = (1 - $\frac{1}{5}$) = $\frac{4}{5}$
Now, $\frac{4}{5}$ work is done by Y in 16 days.
Whole work will be done by Y in (16 x $\frac{5}{4}$) = 20 days.
Therefore X's 1 day's work = $\frac{1}{40}$, Y's 1 day's work = $\frac{1}{20}$
(X + Y)'s 1 day's work = ($\frac{1}{40}$ + $\frac{1}{20}$) = $\frac{3}{40}$
Hence, X and Y will together complete the work in ($\frac{40}{3}$) = 13 $\frac{1}{3}$ days.

### Q3

A and B can do a job together in 7 days. A is 1 3/4 times as efficient as B. The same job can be done by A alone in :
A. 9 days B. 11 days C. 12 days D. 10 days

B
(A's 1 day's work) : (B's 1 day's work) = $\frac{7}{4}$ : 1 = 7 : 4.
Let A's and B's 1 day's work be 7x and 4x respectively.
Then, 7x + 4x = $\frac{1}{7} \rightarrow$ 11x =$\frac{1}{7} \rightarrow$ x = $\frac{1}{77}$
Therefore A's 1 day's work = ($\frac{1}{77}$ x 7) = $\frac{1}{11}$ = 11 days

### Q4

A and B together can do a piece of work in 30 days. A having worked for 16 days, B finishes the remaining work alone in 44 days. In how many days shall B finish the whole work alone?
A. 30 days B. 40 days C. 60 days D. 70 days

C
Let A's 1 day's work = x and B's 1 day's work = y.
Then, x + y = $\frac{1}{30}$ and 16x + 44y = 1.
Solving these two equations, we get: x = $\frac{1}{60}$ and y = $\frac{1}{60}$
B's 1 day's work = $\frac{1}{60}$
Hence, B alone shall finish the whole work in 60 days.

### Q5

If 6 men and 8 boys can do a piece of work in 10 days while 26 men and 48 boys can do the same in 2 days, the time taken by 15 men and 20 boys in doing the same type of work will be:
A. 4 days B. 5 days C. 6 days D. 7 days

A
Let 1 man's 1 day's work = x and 1 boy's 1 day's work = y.
Then, 6x + 8y = $\frac{1}{10}$ and 26x + 48y = $\frac{1}{2}$
Solving these two equations, we get : x = $\frac{1}{100}$and y = $\frac{1}{200}$
(15 men + 20 boy)'s 1 day's work = ($\frac{15}{100}$ + $\frac{20}{200}$) = $\frac{1}{4}$
i.e, 15 men and 20 boys can do the work in 4 days.