Quantitative Aptitude
TIME AND WORK MCQs
Time & Work, Work And Wages
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.
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.
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
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 \(\frac{24}{7}days=3\frac{3}{7}days \)
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.
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.
(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.
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.
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.
(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)