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91. X can do a piece of work in 40 days. He works at it for 8 days and then Y finished it in 16 days. How long will they together take to complete the work?

A. $13 \frac{1}{3}$ days

B. 15 days

C. 20 days

D. 26 days

Discuss

Solution:

Work done by X in 8 days =

\frac{1}{40} \times 8

\frac{1}{5}

Remaining work =

1 - \frac{1}{5}

\frac{4}{5}

Now,

\frac{4}{5}

work is done by Y in 16 days
Whole work will be done by Y in =

16 \times \frac{5}{4}

= 20 days
∴ X's 1 day's work =

\frac{1}{40}

∴ Y's 1 day's work =

\frac{1}{20}

(X + Y)'s 1 day's work

\begin{aligned} = \frac{1}{40} + \frac{1}{20} \\ = \frac{3}{40} \end{aligned}

Hence, X and Y will together complete the work in

\begin{aligned} = \frac{40}{3} \\ = 13 \frac{1}{3} days \end{aligned}

92. A and B can do a job together in 7 days. A is $1 \frac{3}{4}$ times as efficient as B. The same job can be done by A alone in :

A. $9 \frac{1}{3}$ days

B. 11 days

C. $12 \frac{1}{4}$ days

D. $16 \frac{1}{3}$ days

Discuss

Solution:

\begin{aligned} (A's 1 day's work) : (B's 1 day's work) \\ = \frac{7}{4} : 1 = 7 : 4 \\ Let A's and B's 1 day's work be \\ 7 x and 4 x respectively \\ Then, 7 x + 4 x = \frac{1}{7} \\ \Rightarrow 11 x = \frac{1}{7} \\ \Rightarrow x = \frac{1}{77} \\ ∴ A's 1 day's work \\ = \frac{1}{77} \times 7 = \frac{1}{11} \end{aligned}

So, A will do the work in 11 days

93. A and B together can do a piece of work in 30 days. A having worked for 16 days, B finishes the remaining work alone in 44 days. In how many days shall B finish the whole work alone?

A. 30 days

B. 40 days

C. 60 days

D. 70 days

Discuss

Solution:

\begin{aligned} Let A's 1 day's work = x and \\ B's 1 day's work = y \\ Then, x + y = \frac{1}{30} \\ 16 x + 44 y = 1 \\ Solving these two equations, we get \\ x = \frac{1}{60} and y = \frac{1}{60} \\ ∴ B's 1 day's work = \frac{1}{60} \\ Hence, B alone shall finish the \\ whole work in 60 days \end{aligned}

94. A can finish a piece of work in 18 days and B can do the same work in half of the time taken by A. Then working together what part of the same work they can finish in a day ?

A. $\frac{1}{6}$

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

C. $\frac{1}{9}$

D. $\frac{2}{7}$

Discuss

Solution:

So let's solve now,
A's 1 day work =

\frac{1}{18}

B's 1 day work =

\frac{1}{9}

[because B take half time than A]
(A + B)'s one day work

\begin{aligned} = \frac{1}{18} + \frac{1}{9} \\ = \frac{1 + 2}{18} \\ = \frac{1}{6} \end{aligned}

95. A and B can do a piece of work in 72 days, B and C can do it in 120 days and A and C can do it in 90 days. In how many days all three together can do the work ?

A. 80 days

B. 100 days

C. 60 days

D. 150 days

Discuss

Solution:

In these kind of questions, always take total work as L.C.M. of number of days.
Here L.C.M. of Total Work = 360
One day work of A + B =

\frac{360}{72}

= 5 unit/day
One day work of B + C =

\frac{360}{120}

= 3 unit/day
One day work of C + A =

\frac{360}{90}

= 4 unit/day
∴ Total units/day = 5 + 3 + 4 = 12
(Here , 12 unit represents twice of the work done by A, B and C. So we will divide it by 2)
Work done by (A + B + C) per day =

\frac{12}{2}

= 6 units/day
∴Total time taken by (A + B + C)

\begin{aligned} = \frac{360}{6} \\ = 60 days \end{aligned}

96. Ayesha can complete a piece of work in 16 days. Amita can complete the same piece of work in 8 days. If both of them work together in how many days can they complete the same piece of work ?

A. $4 \frac{2}{5} days$

B. $5 \frac{1}{3} days$

C. $6 days$

D. $12 days$

Discuss

Solution:

Ayesha's 1 day's work

= \frac{1}{16}

Amita's 1 day's work

= \frac{1}{8}

(Ayesha + Amitha)'s 1 day's work

\begin{aligned} = \frac{1}{16} + \frac{1}{8} \\ = \frac{3}{16} \end{aligned}

∴ Both together can complete the work in

\begin{aligned} = \frac{16}{3} \\ = 5 \frac{1}{3} days \end{aligned}

97. A can complete a certain work in 4 minutes, B in 5 minutes, C in 6 minutes, D in 10 minutes and E in 12 minutes. The average number of units of work completed by them per minute will be = ?

A. 0.16

B. 0.40

C. 0.80

D. None of these

Discuss

Solution:

\begin{aligned} Required average, \\ = \frac{\frac{1}{4} + \frac{1}{5} + \frac{1}{6} + \frac{1}{10} + \frac{1}{12}}{5} \\ = \frac{48}{60} \times \frac{1}{5} \\ = \frac{4}{25} \\ = 0.16 \end{aligned}

98. A daily-wages labourer was engaged for a certain number of days for Rs. 5750, but being absent on some of those days he paid only Rs. 5000. What were his maximum possible daily wages ?

A. Rs. 125

B. Rs. 250

C. Rs. 375

D. Rs. 500

Discuss

Solution:

Try to solve these kind of question by option
Because of his being absent he was paid Rs. 750 less
Now check with option
Since maximum possible daily wages is asked so it will be Rs. 250
OR :
Maximum possible daily wage
= HCF of Rs. 5750 and Rs. 5000
= Rs. 250

99. A and B together can do a piece of work in 8 days, B and C together in 10 days, while C and A together in 6 days, if they all work together the work will be completed in ?

A. $3 \frac{3}{4} days$

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

C. $5 \frac{5}{47} days$

D. $4 \frac{4}{9} days$

Discuss

Solution:

In these kind of questions, always take total work as L.C.M. of number of days
Here L.C.M. of Total Work = 120
One day work of A + B =

\frac{120}{8}

= 15 unit/day
One day work of B + C =

\frac{120}{10}

= 12 unit/day
One day work of C + A =

\frac{120}{6}

= 20 unit/day
∴ Total units per day = 15 + 12 + 20 = 47
∴ Efficiency of :

\begin{aligned} 2 (A + B + C) = 47 \\ A + B + C = \frac{47}{2} \end{aligned}

(A + B + C) will complete the whole work in

\begin{aligned} = \frac{120}{\frac{47}{2}} \\ = \frac{240}{47} \\ = 5 \frac{5}{47} days \end{aligned}

100. A and B together can complete a piece of work in 8 days, B alone can complete that work in 12 days. B alone worked for four days. After that how long will A alone takes to complete the work ?

A. 15 days

B. 18 days

C. 16 days

D. 20 days

Discuss

Solution:

L.C.M. of total work = 24
One day work of A + B =

\frac{24}{8}

= 3 unit/day
B's 1 day work =

\frac{24}{12}

= 2 units/days
A's 1 day work = 3 - 2 = 1 units/days
4 days work of B = 4 × 2 = 8 units/days
Work left = 24 - 8 = 16 units
A will complete the remaining work in

\begin{aligned} = \frac{16 units}{1 unit/day} \\ = 16 days \end{aligned}

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