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TIME AND WORK MCQs

Time & Work, Work And Wages

Total Questions : 1512 | Page 6 of 152 pages
Question 51.

X and Y can do a piece of work in 20 days and 12 days respectively. X started the work alone and then after 4 days Y joined him till the completion of the work. How long did the work last?

  1.    6 days
  2.    10 days
  3.    15 days
  4.    20 days
 Discuss Question
Answer: Option B. -> 10 days

Work done by X in 4 days = \(\left(\frac{1}{20}\times4\right)=\frac{1}{5}\)


Remaining work = \(\left(1-\frac{1}{5}\right) =\frac{4}{5}\)


(X + Y)'s 1 day's work = \(\left(\frac{1}{20}+\frac{1}{12}\right)=\frac{8}{60}=\frac{2}{15}
\)


Now, \(\frac{2}{15}
\)
  work is done by X and Y in 1 day.


So,  \(\frac{4}{5}\)  work will be done by X and Y in \(\left(\frac{15}{2}\times\frac{4}{5}\right)= 6 days.\)


Hence, total time taken = (6 + 4) days = 10 days.

Question 52.

A is 30% more efficient than B. How much time will they, working together, take to complete a job which A alone could have done in 23 days?

  1.    11 days
  2.    13 days
  3.    \(20\frac{3}{17}days\)
  4.    None of these
 Discuss Question
Answer: Option B. -> 13 days

Ratio of times taken by A and B = 100 : 130 = 10 : 13.


Suppose B takes x days to do the work.


Then, 10 : 13 :: 23 : x     \(\Rightarrow\left(\frac{23\times13}{10}\right) \Rightarrow x=\frac{299}{10}\)


A's 1 day's work = \(\frac{1}{23}\)


B's 1 day's work = \(\frac{10}{299}\)


(A + B)'s 1 day's work = \(\left(\frac{1}{23}+\frac{10}{299}\right)=\frac{23}{299}=\frac{1}{13}\)


Therefore, A and B together can complete the work in 13 days.

Question 53.

Ravi and Kumar are working on an assignment. Ravi takes 6 hours to type 32 pages on a computer, while Kumar takes 5 hours to type 40 pages. How much time will they take, working together on two different computers to type an assignment of 110 pages?

  1.    7 hours 30 minutes
  2.    8 hours
  3.    8 hours 15 minutes
  4.    8 hours 25 minutes
 Discuss Question
Answer: Option C. -> 8 hours 15 minutes

Number of pages typed by Ravi in 1 hour = \(\frac{32}{6}=\frac{16}{3}\)


Number of pages typed by Kumar in 1 hour = \(\frac{40}{5}=8\)


Number of pages typed by both in 1 hour = \(\left(\frac{16}{3}+8\right)= \frac{40}{3}\)


So, Time taken by both to type 110 pages =  \(\left(110\times\frac{3}{40}\right) hours\)


=  \(8\frac{1}{4}\)  hours (or) 8 hours 15 minutes

Question 54.

A, B and C can complete a piece of work in 24, 6 and 12 days respectively. Working together, they will complete the same work in:

  1.    \(\frac{1}{24}day\)
  2.    \(\frac{7}{24}day\)
  3.    \(3\frac{3}{7}days \)
  4.    4 days
 Discuss Question
Answer: Option C. -> \(3\frac{3}{7}days \)

Formula: If A can do a piece of work in n days, then A's 1 day's work =  \(\frac{1}{n},\)


(A + B + C)'s 1 day's work = \(\left(\frac{1}{24}+\frac{1}{6}+\frac{1}{12}\right)=\frac{7}{24}\)


Formula: If A's 1 day's work = \(\frac{1}{n},\)  then A can finish the work in n days.


So, all the three together will complete the job in \(\frac{24}{7}days=3\frac{3}{7}days \)

Question 55.

Sakshi can do a piece of work in 20 days. Tanya is 25% more efficient than Sakshi. The number of days taken by Tanya to do the same piece of work is:

  1.    15
  2.    16
  3.    18
  4.    25
 Discuss Question
Answer: Option B. -> 16

Ratio of times taken by Sakshi and Tanya = 125 : 100 = 5 : 4.


Suppose Tanya takes x days to do the work.


5 : 4 :: 20 : x    \(\Rightarrow\left(\frac{4\times20}{5}\right)\)


 x = 16 days.


Hence, Tanya takes 16 days to complete the work.

Question 56.

A takes twice as much time as B or thrice as much time as C to finish a piece of work. Working together, they can finish the work in 2 days. B can do the work alone in:

  1.    4 days
  2.    6 days
  3.    8 days
  4.    12 days
 Discuss Question
Answer: Option B. -> 6 days

Suppose A, B and C take x,   \(\frac{x}{2}and\frac{x}{3}\)  days respectively to finish the work.


Then,  \(\left(\frac{1}{x}+\frac{2}{x}+\frac{3}{x}\right) =\frac{1}{2}\)


\(\frac{6}{x}=\frac{1}{2}\)


 x = 12.


So, B takes (12/2) = 6 days to finish the work.

Question 57.

A and B can complete a work in 15 days and 10 days respectively. They started doing the work together but after 2 days B had to leave and A alone completed the remaining work. The whole work was completed in :

  1.    8 days
  2.    10 days
  3.    12 days
  4.    15 days
 Discuss Question
Answer: Option C. -> 12 days

(A + B)'s 1 day's work =   \(\left(\frac{1}{15}+\frac{1}{10}\right) =\frac{1}{6}\)


Work done by A and B in 2 days = \(\left(\frac{1}{6}\times2\right) = \frac{1}{3}\)


Remaining work = \(\left(1-\frac{1}{3}\right)=\frac{2}{3} \)


Now,  \(\frac{1}{15}\) work is done by A in 1 day.


 So,   \(\frac{2}{3}\)   work will be done by a in    \(\left(15\times\frac{2}{3}\right)\) = 10 days.


Hence, the total time taken = (10 + 2) = 12 days.

Question 58.

A and B can do a piece of work in 30 days, while B and C can do the same work in 24 days and C and A in 20 days. They all work together for 10 days when B and C leave. How many days more will A take to finish the work?

  1.    18 days
  2.    24 days
  3.    30 days
  4.    36 days
 Discuss Question
Answer: Option A. -> 18 days

2(A + B + C)'s 1 day's work = \(\left(\frac{1}{30}+\frac{1}{24}+\frac{1}{20}\right) =\frac{15}{120}=\frac{1}{8}.\)


Therefore, (A + B + C)'s 1 day's work =  \(\frac{1}{2\times8}=\frac{1}{16}\)


Work done by A, B, C in 10 days =  \(\frac{10}{16}=\frac{5}{8}\)


Remaining work =  \(\left(1-\frac{5}{8}\right)=\frac{3}{8}\)


A's 1 day's work = \(\left(\frac{1}{16}-\frac{1}{24}\right)=\frac{1}{48}\)


Now,   \(\frac{1}{48}\)  work is done by A in 1 day.


So,   \(\frac{3}{8}\)    work will be done by A in     \(\left(48\times\frac{3}{8}\right)\)    =  18 days.

Question 59.

A works twice as fast as B. If B can complete a work in 12 days independently, the number of days in which A and B can together finish the work in :

  1.    4 days
  2.    6 days
  3.    8 days
  4.    18 days
 Discuss Question
Answer: Option A. -> 4 days

Ratio of rates of working of A and B = 2 : 1.


So, ratio of times taken = 1 : 2.


B's 1 day's work =  \(\frac{1}{12}\)


So, A's 1 day's work =  \(\frac{1}{6}\)  ; (2 times of B's work)


(A + B)'s 1 day's work = \(\left(\frac{1}{6}+\frac{1}{12}\right)=\frac{3}{12}=\frac{1}{4}.\)


So, A and B together can finish the work in 4 days.

Question 60.

Twenty women can do a work in sixteen days. Sixteen men can complete the same work in fifteen days. What is the ratio between the capacity of a man and a woman?

  1.    3 : 4
  2.    4 : 3
  3.    5 : 3
  4.    Data inadequate
 Discuss Question
Answer: Option B. -> 4 : 3

(20 x 16) women can complete the work in 1 day.


 So, 1 woman's 1 day's work = \(\frac{1}{320}\)


(16 x 15) men can complete the work in 1 day.


so, 1 man's 1 day's work =  \(\frac{1}{240}\)


So, required ratio  =  \(\frac{1}{240}:\frac{1}{320}\)


\(\frac{1}{3}:\frac{1}{4}\)


= 4 : 3 (cross multiplied)

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