Practice MCQ Questions and Answer on Time and Work

101.

George takes 8 hours to copy a 50-page manuscript while Sonia can copy the same manuscript in 6 hours. How many hours would it take them to copy a 100-page manuscript, if they work together ?

(A) $6 \frac{6}{7} hours$
(B) $9 hours$
(C) $9 \frac{5}{7} hours$
(D) $14 hours$

Solution: Number of pages typed by Gorge in 1 hour $\begin{aligned} = \frac{50}{8} \\ = \frac{25}{4} \end{aligned}$ Number of pages typed by Sonia in 1 hour $\begin{aligned} = \frac{50}{6} \\ = \frac{25}{3} \end{aligned}$ Number of pages typed by Gorge and Sonia together in 1 hour $\begin{aligned} = (\frac{25}{4} + \frac{25}{3}) \\ = (\frac{75 + 100}{12}) \\ = \frac{175}{12} \\ ∴ Required time \\ = (100 \div \frac{175}{12}) hours \\ = (\frac{100 \times 12}{175}) hours \\ = \frac{48}{7} hours \\ = 6 \frac{6}{7} hours \end{aligned}$

102.

A can lay railway track between two given stations in 16 days and B can do the same job in 12 days. With the help of C, they did the job in 4 days only. Then, C alone can do the job in ?

(A) $9 \frac{1}{5} days$
(B) $9 \frac{2}{5} days$
(C) $9 \frac{3}{5} days$
(D) $10 days$

Solution: $\begin{aligned} (A + B + C)'s 1 day's work = \frac{1}{4} \\ A's 1 day's work = \frac{1}{16} \\ B's 1 day's work = \frac{1}{12} \\ ∴ C's 1 day's work \\ = \frac{1}{4} - (\frac{1}{16} + \frac{1}{12}) \\ = (\frac{1}{4} - \frac{7}{48}) \\ = \frac{5}{48} \\ So, C alone can do the work in \\ = \frac{48}{5} \\ = 9 \frac{3}{5} days \end{aligned}$

103.

A can do 20% of work in 4 days, B can do $33 \frac{1}{3} %$ ÃÂÃÂ of the same work in 10 days. They worked together for 9 days. C completed the remaining work in 6 days. B and C together complete 75% of the same work in:

(A) 9 days
(B) 15 days
(C) 10 days
(D) 12 days

Solution: A = 20 days B = 30 days (A + B) × 9 + C × 6 = 60 (3 + 2) × 9 + C × 6 = 60 C = $\frac{5}{2}$ unit C = $\frac{60 \times 2}{5}$ = 24 days (B + C) × x = 60 × $\frac{3}{4}$ $(2 + \frac{5}{2}) x = 45$ 9x = 90 x = 10 days

104.

A can do a certain job in 12 days and B is 60% more efficient than A. The B can do the same piece of work in ?

(A) $8 days$
(B) $7 \frac{1}{2} days$
(C) $6 \frac{1}{4} days$
(D) $6 days$

Solution: Ratio of time, taken by A and B = 160 : 100 = 8 : 5 If A takes 8 days, B takes 5 days If A takes 12 days, B takes $= \frac{5}{8} \times 12 = \frac{15}{2} = 7 \frac{1}{2}$ days

105.

Three men A, B, C working together can do a job in 6 hours less time than A alone, in one hour less time than B alone and in one half the time needed by C when working alone. Then A and B together can do the job in:

(A) $\frac{2}{3}$ hours
(B) $\frac{3}{4}$ hours
(C) $\frac{3}{2}$ hours
(D) $\frac{4}{3}$ hours

Solution: Time taken by A =x hours. Therefore taken by A, B and C together = (x - 6) Time taken by B = (x - 5) Time taken by C = 2(x - 6) Now, rate of work of A + Rate of work of B + Rate of work of C = Rate of work of ABC. $\Rightarrow \frac{1}{x} + \frac{1}{x - 5} + \frac{1}{2 (x - 6)} = \frac{1}{x - 6}$ On solving above equation, we get x = 3, $\frac{40}{6}$ When x = 3, the expression (x - 6) becomes negative, thus it's not possible. $\Rightarrow x = \frac{40}{6}$ Time taken by A & B together = $\frac{1}{\frac{3}{20} + \frac{3}{5}}$ = $\frac{4}{3}$ hours

106.

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?

(A) 23 days
(B) 37 days
(C) $37 \frac{1}{2}$ days
(D) 40 days

Solution: $\begin{aligned} Whole work is done by A in \\ = 20 \times \frac{5}{4} = 25 days \\ Now, (1 - \frac{4}{5}) i . e ., \\ \frac{1}{5} work is done by A and B in 3 days \\ Whole work will be done by A and B in \\ = (3 \times 5) = 15 days \\ A's 1 day's work = \frac{1}{25}, \\ (A + B)'s 1 day's work = \frac{1}{15} \\ ∴ B's 1 day's work \\ = \frac{1}{15} - \frac{1}{25} = \frac{4}{150} = \frac{2}{75} \\ So, B alone would do the work in \\ \frac{75}{2} = 37 \frac{1}{2} days \end{aligned}$

107.

A, B and C can do a piece of work in 20, 30 and 60 days respectively. In how many days can A do the work if he is assisted by B and C on every third day?

(A) 12 days
(B) 15 days
(C) 16 days
(D) 18 days

Solution: $\begin{aligned} A's 2 day's work = \frac{1}{20} \times 2 = \frac{1}{10} \\ (A + B + C)'s 1 day's work \\ = \frac{1}{20} + \frac{1}{30} + \frac{1}{60} = \frac{6}{60} = \frac{1}{10} \\ Work done in 3 days = \frac{1}{10} + \frac{1}{10} = \frac{1}{5} \\ Now, \frac{1}{5} work is done in 3 days \\ ∴ Whole work will be done in \\ 3 \times 5 = 15 days \end{aligned}$

108.

3 men and 4 women can do a piece of work in 7 days, whereas 2 men and 1 woman can do it in 14 days. 7 women will complete the same work in:

(A) 10 days
(B) 8 days
(C) 9 days
(D) 12 days

Solution: (3m + 4w) × 7 = (2m + 1w) × 14 3m + 4w = 4m + 2w m = 2w m : w = 2 : 1 Total work = (3 × 2 + 4 × 1) × 7 = 70 unit 7w = 70 unit = $\frac{70}{7}$ = 10 days

109.

60 men could complete a piece of work in 250 days. They worked together for 200 days. After that work had to be stopped for 10 days due to bad weather. How many more men should be engaged to complete the work in time ?

(A) 10
(B) 15
(C) 18
(D) 20

110.

A can do a certain work in 12 days. B is 60% more efficient then A. How many days will B and A together take to do the same job?

(A) $\frac{80}{13} days$
(B) $\frac{70}{13} days$
(C) $\frac{75}{13} days$
(D) $\frac{60}{13} days$

Solution: Time taken by B to complete the work $\begin{aligned} = 12 \times \frac{100}{160} \\ = \frac{15}{2} days \end{aligned}$ ∴ (A + B)'s 1 day's work $\begin{aligned} = \frac{1}{12} + \frac{2}{15} \\ = \frac{5 + 8}{60} \\ = \frac{13}{60} \end{aligned}$ Hence, the work will be completed in $\frac{60}{13}$ days Alternate: Ratio of time, taken by A and B = 160 : 100 = 8 : 5 If A takes 8 days, B takes 5 days. If A takes 12 days, B takes = $\frac{5}{8} \times 12 = \frac{15}{2}$ Time take by A = 12 days Time take by B = 7.5 days L.C.M. of Total Work = 60 Ratio of time, taken by A and B = 8 : 5 Time taken by A and B together to complete the task $= \frac{60}{13} days$

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Practice MCQ Questions and Answer on Time and Work

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