Quantitative Aptitude
TIME AND WORK MCQs
Time & Work, Work And Wages
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.
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.
(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.
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.
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 ?
(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.
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.
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.
(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.
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 = \(\left(\frac{480}{11}\times\frac{1}{8}\right)= \frac{60}{11}days = 5\frac{5}{11}days.\)
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.