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Quantitative Aptitude

TIME AND WORK MCQs

Time & Work, Work And Wages

Total Questions : 1512 | Page 5 of 152 pages
Question 41.

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:

  1.    4 days
  2.    5 days
  3.    6 days
  4.    7 days
 Discuss Question
Answer: Option A. -> 4 days

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 = \(\left(\frac{15}{100}+\frac{20}{200}\right)=\frac{1}{4}.\)


 so, 15 men and 20 boys can do the work in 4 days.

Question 42.

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?

  1.    8 hours
  2.    10 hours
  3.    12 hours
  4.    24 hours
 Discuss Question
Answer: Option C. -> 12 hours

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 =  \(\left(\frac{1}{4}+\frac{1}{3}\right)=\frac{7}{12}.\)


B's 1 hour's work =  \(\left(\frac{7}{12}-\frac{1}{2}\right)=\frac{1}{12}.\)


So, B alone will take 12 hours to do the work.

Question 43.

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:

  1.    15 days
  2.    20 days
  3.    25 days
  4.    30 days
 Discuss Question
Answer: Option C. -> 25 days

(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 = \(\left(\frac{1}{10}+\frac{1}{50}\right)=\frac{6}{50}= \frac{3}{25}. ......(i)\)


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) = \(\frac{3}{25}\)


A's 1 day's work =  \(\frac{3}{50}\)


So, B's 1 day's work \(\left(\frac{1}{10}-\frac{3}{50}\right)=\frac{2}{50} = \frac{1}{25}.\)


So, B alone could do the work in 25 days.

Question 44.

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?

  1.    23 days
  2.    37 days
  3.    \(37^{\frac{1}{2}}\)
  4.    40 days
 Discuss Question
Answer: Option C. -> \(37^{\frac{1}{2}}\)

Whole work is done by A in  \( \left(20\times\frac{5}{4}\right)\) = 25 days.


Now,  \( \left(1-\frac{5}{4}\right)\) 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.


A's 1 day's work = \(\frac{1}{25}\)  ,  (A + B)'s 1 day's work = \(\frac{1}{15}\)


So, B's 1 day's work = \( \left(\frac{1}{15}-\frac{1}{25}\right)=\frac{4}{150}=\frac{2}{75}\)


So, B alone would do the work in  \( \frac{75}{2}.\)  =  \( 37^{\frac{1}{2}}\)  days.

Question 45.

A machine P can print one lakh books in 8 hours, machine Q can print the same number of books in 10 hours while machine R can print them in 12 hours. All the machines are started at 9 A.M. while machine P is closed at 11 A.M. and the remaining two machines complete work. Approximately at what time will the work (to print one lakh books) be finished ?

  1.    11:30 A.M.
  2.    12 noon
  3.    12:30 P.M.
  4.    1:00 P.M.
 Discuss Question
Answer: Option D. -> 1:00 P.M.

(P + Q + R)'s 1 hour's work = \(\left(\frac{1}{8}+\frac{1}{10}+\frac{1}{12}\right) = \frac{37}{120}\)


Work done by P, Q and R in 2 hours = \(\left(\frac{37}{120}\times2\right) = \frac{37}{60}\)


Remaining work = \(\left(1-\frac{37}{60}\right) = \frac{23}{60}\)


(Q + R)'s 1 hour's work = \( \left(\frac{1}{10}+\frac{1}{12}\right)=\frac{11}{60}\)


Now, \(\frac{11}{60}\)   work is done by Q and R in 1 hour.


So,   \(\frac{23}{60}\)  work will be done by Q and R in      \(\left(\frac{60}{11}\times \frac{23}{60}\right) = \frac{23}{11}
\)
    hours appx. 2 hours.


So, the work will be finished approximately 2 hours after 11 A.M., i.e., around 1 P.M.

Question 46.

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?

  1.    5
  2.    \(5\frac{1}{2}\)
  3.    6
  4.    8
 Discuss Question
Answer: Option C. -> 6

B's 10 day's work = \(\left(\frac{1}{5}\times10\right) = \frac{2}{3}.\)


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


Now,  \(\frac{1}{18}\)  work is done by A in 1 day.


So,  \(\frac{1}{3}\)  work is done by A in  \( \left(18\times\frac{1}{3}\right)\)  = 6 days.

Question 47.

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?

  1.    35
  2.    40
  3.    45
  4.    50
 Discuss Question
Answer: Option B. -> 40

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 =  \(\frac{1}{400}\)   , y =    \(\frac{1}{400}\)


So, 1 woman's 1 day's work =  \(\frac{1}{400}\)


10 women's 1 day's work = \(\left(\frac{1}{400}\times10\right) = \frac{1}{40}.\)


Hence, 10 women will complete the work in 40 days.

Question 48.

A and B can together finish a work 30 days. They worked together for 20 days and then B left. After another 20 days, A finished the remaining work. In how many days A alone can finish the work?

  1.    40
  2.    50
  3.    54
  4.    60
 Discuss Question
Answer: Option D. -> 60

(A + B)'s 20 day's work = \(\left(\frac{1}{30}\times20\right) = \frac{2}{3}.\)


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


Now,  \(\frac{1}{3}\)   work is done by A in 20 days.


Therefore, the whole work will be done by A in (20 x 3) = 60 days.

Question 49.

P can complete a work in 12 days working 8 hours a day. Q can complete the same work in 8 days working 10 hours a day. If both P and Q work together, working 8 hours a day, in how many days can they complete the work?

  1.    \(5\frac{5}{11}\)
  2.    \(5\frac{6}{11}\)
  3.    \(6\frac{5}{11}\)
  4.    \( 6\frac{6}{11}\)
 Discuss Question
Answer: Option A. -> \(5\frac{5}{11}\)

P can complete the work in (12 x 8) hrs. = 96 hrs.


Q can complete the work in (8 x 10) hrs. = 80 hrs.


So, P's1 hour's work =   \(\frac{1}{96}\)  and Q's 1 hour's work =  \(\frac{1}{80}\) 


(P + Q)'s 1 hour's work =  \(\left(\frac{1}{96}+\frac{1}{80}\right)= \frac{11}{480}\)


So, both P and Q will finish the work in \(\left(\frac{480}{11}\right)\)  hrs.


Therefore, Number of days of 8 hours each = \(\left(\frac{480}{11}\times\frac{1}{8}\right)= \frac{60}{11}days = 5\frac{5}{11}days.\)

Question 50.

10 women can complete a work in 7 days and 10 children take 14 days to complete the work. How many days will 5 women and 10 children take to complete the work?

  1.    3
  2.    5
  3.    7
  4.    Cannot be determined
  5.    None of these
 Discuss Question
Answer: Option C. -> 7

1 woman's 1 day's work =  \(\frac{1}{70}\)


1 child's 1 day's work = \(\frac{1}{140}\)


5 women + 10 children)'s day's work =  \(\left(\frac{5}{70}+\frac{10}{140}\right)=\left(\frac{1}{14}+\frac{1}{14}\right) =\frac{1}{7}\)


So,  5 women and 10 children will complete the work in 7 days.

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