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81. Ravi and Kumar are working on an assignment. Ravi takes 6 hours to type 32 pages on a computer, while Kumar takes 5 hours to type 40 pages. How much time will they take, working together on two different computers to type an assignment of 110 pages?

A. 7 hours 30 minutes

B. 8 hours

C. 8 hours 15 minutes

D. 8 hours 25 minutes

Discuss

Solution:

\begin{aligned} 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 \\ = \frac{16}{3} + 8 = \frac{40}{3} \\ ∴ Time taken by both to type 110 pages \\ = 110 \times \frac{3}{40} hours \\ = 8 \frac{1}{4} hours (or) 8 hours 15 minutes \end{aligned}

82. A, B and C can complete a piece of work in 24, 6 and 12 days respectively. Working together, they will complete the same work in:

A. $\frac{1}{24}$ day

B. $\frac{7}{24}$ day

C. $3 \frac{3}{7}$ days

D. 4 days

Discuss

Solution:

Formula: If A can do a piece of work in n days, then A's 1 day's work =

\frac{1}{n}

\begin{aligned} (A + B + C)^{'} s 1 day's work \\ = \frac{1}{24} + \frac{1}{6} + \frac{1}{12} = \frac{7}{24} \end{aligned}

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

83. Sakshi can do a piece of work in 20 days. Tanya is 25% more efficient than Sakshi. The number of days taken by Tanya to do the same piece of work is:

A. 15

B. 16

C. 18

D. 25

Discuss

Solution:

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
⇒

x = \frac{4 \times 20}{5}

⇒ x = 16 days
Hence, Tanya takes 16 days to complete the work

84. A takes twice as much time as B or thrice as much time as C to finish a piece of work. Working together, they can finish the work in 2 days. B can do the work alone in:

A. 4 days

B. 6 days

C. 8 days

D. 12 days

Discuss

Solution:

\begin{aligned} Suppose A, B and C take \\ x, \frac{x}{2}, \frac{x}{3} days respectively to finish the work \\ Then, \frac{1}{x} + \frac{2}{x} + \frac{3}{x} = \frac{1}{2} \\ \Rightarrow \frac{6}{x} = \frac{1}{2} \\ \Rightarrow x = 12 \\ So, B takes \frac{12}{2} \\ = 6 days to finish the work \end{aligned}

85. A and B can complete a work in 15 days and 10 days respectively. They started doing the work together but after 2 days B had to leave and A alone completed the remaining work. The whole work was completed in :

A. 8 days

B. 10 days

C. 12 days

D. 15 days

Discuss

Solution:

\begin{aligned} (A + B)'s 1 day's work \\ = \frac{1}{15} + \frac{1}{10} = \frac{1}{6} \\ Work done by A and B in 2 days \\ = \frac{1}{6} \times 2 = \frac{1}{3} \\ Remaining work \\ = 1 - \frac{1}{3} = \frac{2}{3} \\ Now, \frac{1}{15} work is done by A in 1 day \\ ∴ \frac{2}{3} work will be done by a in \\ 15 \times \frac{2}{3} = 10 days \\ Hence, the total time taken \\ = 10 + 2 = 12 days \end{aligned}

86. A and B can do a piece of work in 30 days, while B and C can do the same work in 24 days and C and A in 20 days. They all work together for 10 days when B and C leave. How many days more will A take to finish the work?

A. 18 days

B. 24 days

C. 30 days

D. 36 days

Discuss

Solution:

\begin{aligned} 2(A + B + C)'s 1 day's work \\ = \frac{1}{30} + \frac{1}{24} + \frac{1}{20} \\ = \frac{15}{120} = \frac{1}{8} \\ ∴ (A + B + C)'s 1 day's work \\ = \frac{1}{2 \times 8} = \frac{1}{16} \\ Work done by A, B, C in 10 days \\ = \frac{10}{16} = \frac{5}{8} \\ Remaining work \\ = 1 - \frac{5}{8} = \frac{3}{8} \\ A's 1 day's work \\ = \frac{1}{16} - \frac{1}{24} = \frac{1}{48} \\ Now, \frac{1}{48} work isdone by A in 1 day \\ So, \frac{3}{8} work will be done by A in \\ 48 \times \frac{3}{8} = 18 days \end{aligned}

87. A works twice as fast as B. If B can complete a work in 12 days independently, the number of days in which A and B can together finish the work in :

A. 4 days

B. 6 days

C. 8 days

D. 18 days

Discuss

Solution:

\begin{aligned} Ration 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} \\ ∴ A's 1 day's work \\ = \frac{1}{3}; (2 times of B's work) \\ (A + B)'s 1 day's work \\ = \frac{1}{6} + \frac{1}{12} = \frac{3}{12} = \frac{1}{4} \\ So, A and B together can finish the \\ work in 4 days . \end{aligned}

88. Twenty women can do a work in sixteen days. Sixteen men can complete the same work in fifteen days. What is the ratio between the capacity of a man and a woman?

A. 3 : 4

B. 4 : 3

C. 5 : 3

D. Data inadequate

Discuss

Solution:

\begin{aligned} (20 \times 16) women can complete the work in 1 day \\ ∴ 1 woman's 1 day's work = \frac{1}{320} \\ (16 \times 15) men can complete the work in 1 day \\ ∴ 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) \end{aligned}

89. A and B can do a work in 8 days, B and C can do the same work in 12 days. A, B and C together can finish it in 6 days. A and C together will do it in :

A. 4 days

B. 6 days

C. 8 days

D. 12 days

Discuss

Solution:

\begin{aligned} (A + B + C)'s 1 day's work = \frac{1}{6} \\ (A + B)'s 1 day's work = \frac{1}{8} \\ (B + C)'s 1 day's work = \frac{1}{12} \\ ∴ (A + C)'s 1 day's work \\ = (2 \times \frac{1}{6}) - (\frac{1}{8} + \frac{1}{12}) \\ = \frac{1}{3} - \frac{5}{24} \\ = \frac{3}{24} \\ = \frac{1}{8} \end{aligned}

So, A and C together will do the work in 8 days

90. A can finish a work in 24 days, B in 9 days and C in 12 days. B and C start the work but are forced to leave after 3 days. The remaining work was done by A in:

A. 5 days

B. 6 days

C. 10 days

D. $10 \frac{1}{2}$ days

Discuss

Solution:

\begin{aligned} (B + C)'s 1 day's work \\ = \frac{1}{9} + \frac{1}{12} = \frac{7}{36} \\ Work done by B and C in 3 days \\ = \frac{7}{36} \times 3 = \frac{7}{12} \\ Remaining work \\ = 1 - \frac{7}{12} = \frac{5}{12} \\ Now, \frac{1}{24} work is done by A in 1 day \\ So, \frac{5}{12} work is done by A in \\ 24 \times \frac{5}{12} = 10 days \end{aligned}

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