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71. 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:

A. 15 days

B. 20 days

C. 25 days

D. 30 days

Discuss

Solution:

\begin{aligned} (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 \\ = \frac{1}{10} + \frac{1}{50} = \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 \times (A's 1 day's work) \\ = \frac{3}{25} \\ \Rightarrow A's 1 day's work = \frac{3}{50} \\ ∴ B's 1 day's work (\frac{1}{10} - \frac{3}{50}) \\ = \frac{2}{50} = \frac{1}{25} \\ So, B alone could do the work in 25 days \end{aligned}

72. 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

Discuss

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}

73. 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 ?

A. 11:30 A.M.

B. 12 Noon

C. 12:30 P.M.

D. 1:00 P.M.

Discuss

Solution:

\begin{aligned} (P + Q + R)'s 1 hour's work \\ = \frac{1}{8} + \frac{1}{10} + \frac{1}{12} = \frac{37}{120} \\ Work done by P, Q and R in 2 hours \\ = \frac{37}{120} \times 2 = \frac{37}{60} \\ Remaining work = 1 - \frac{37}{60} = \frac{23}{60} \\ (Q + R)'s 1 hour's work \\ = \frac{1}{10} + \frac{1}{12} = \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 \\ = \frac{60}{11} \times \frac{23}{60} = \frac{23}{11} hours \approx 2 hours \\ So, the work will be finished approximately \\ 2 hours after 11 A .M ., i .e ., around 1 P .M . \end{aligned}

74. 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?

A. 5

B. $5 \frac{1}{2}$

C. 6

D. 8

Discuss

Solution:

\begin{aligned} B's 10 day's work \\ = \frac{1}{15} \times 10 = \frac{2}{3} \\ Remaining work \\ = 1 - \frac{2}{3} = \frac{1}{3} \\ Now, \frac{1}{18} work is done by A in 1 day \\ ∴ \frac{1}{3} work is done by A in \\ 18 \times \frac{1}{3} = 6 days \end{aligned}

75. 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?

A. 35

B. 40

C. 45

D. 50

Discuss

Solution:

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{11}{400}, y = \frac{1}{400}

∴ 1 woman's 1 day's work =

\frac{1}{400}

⇒ 10 women's 1 day's work =

\frac{1}{400} \times 10

\frac{1}{40}

Hence, 10 women will complete the work in 40 days

76. 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?

A. 40

B. 50

C. 54

D. 60

Discuss

Solution:

\begin{aligned} (A + B)'s 20 day's work \\ = \frac{1}{30} \times 20 = \frac{2}{3} \\ Remaining work \\ = 1 - \frac{2}{3} = \frac{1}{3} \\ Now, \frac{1}{3} work is done by A in 20 days \\ ∴ The whole work will be done by A in \\ 20 \times 3 = 60 d a y s \end{aligned}

77. 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?

A. $5 \frac{5}{11}$

B. $5 \frac{6}{11}$

C. $6 \frac{5}{11}$

D. $6 \frac{6}{11}$

Discuss

Solution:

\begin{aligned} P can complete the work \\ = (12 \times 8) hrs . = 96 hrs . \\ Q can complete the work \\ = (8 \times 10) hrs . = 80 hrs . \\ ∴ P's 1 hour's work = \frac{1}{96} and \\ ∴ Q's 1 hour's work = \frac{1}{80} \\ (P + Q)'s 1 hour's work \\ = \frac{1}{96} + \frac{1}{80} = \frac{11}{480} \\ So, both P and Q will finish the work \\ = \frac{480}{11} hrs . \\ ∴ Number of days of 8 hours each \\ \frac{480}{11} \times \frac{1}{8} = \frac{60}{11} days = 5 \frac{5}{11} days \end{aligned}

78. 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?

A. 3

B. 5

C. 7

D. Cannot be determined

Discuss

Solution:

\begin{aligned} 1 w o m a n^{'} s 1 d a y^{'} s w o r k = \frac{1}{70} \\ 1 child's 1 day's work = \frac{1}{140} \\ (5 women + 10 children)'s day's work \\ = \frac{5}{70} + \frac{10}{140} = \frac{1}{14} + \frac{1}{14} = \frac{1}{7} \\ ∴ 5 women and 10 chidren will complete \\ the work in 7 days \end{aligned}

79. 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?

A. 6 days

B. 10 days

C. 15 days

D. 20 days

Discuss

Solution:

\begin{aligned} work done by X in 4 days \\ = \frac{1}{20} \times 4 = \frac{1}{5} \\ Remaining work \\ = 1 - \frac{1}{5} = \frac{4}{5} \\ (X + Y)'s 1 day's work \\ = \frac{1}{20} + \frac{1}{12} = \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 \\ \frac{15}{2} \times \frac{4}{5} = 6 days \\ Hence, total time taken \\ = (6 + 4) days \\ = 10 days \end{aligned}

80. 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?

A. 11 days

B. 13 days

C. $20 \frac{3}{17}$ days

D. None of these

Discuss

Solution:

\begin{aligned} 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 x = \frac{23 \times 13}{10} \\ \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 \\ = \frac{1}{23} + \frac{10}{299} \\ = \frac{23}{299} \\ = \frac{1}{13} \\ ∴ A and B together can complete \\ the work in 13 days . \end{aligned}

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