Time And Work - Aptitude MCQ Questions and Solutions with Explanations

$$\eqalign{ & {\text{1 men's 1 day's work}} \cr & = \frac{1}{{99 \times 2}} \cr & = \frac{1}{{198}} \cr & {\text{1 women's 1 day's work}} \cr & = \frac{1}{{99 \times 6}}. \cr & = \frac{1}{{594}} \cr & {\text{1 boy's 1 day's work}} \cr & = \frac{1}{{99 \times 4}} \cr & = \frac{1}{{396}} \cr} $$
(1 men + 1 women + boy)'s 1 day's work
$$\eqalign{ & = \frac{1}{{198}} + \frac{1}{{594}} + \frac{1}{{396}} \cr & = \frac{{11}}{{1188}} \cr & = \frac{1}{{108}} \cr} $$
Hence, 1 mens , 1 women and 1 boys together take 108 days to finish the work.

$$\eqalign{ & {\text{1 men's 1 day's work}} \cr & = \frac{1}{{20 \times 8}} \cr & = \frac{1}{{160}} \cr & {\text{1 women's 1 day's work}} \cr & = \frac{1}{{32 \times 8}} \cr & = \frac{1}{{256}} \cr & \left( {{\text{5 men}} + {\text{8 women}}} \right){\text{'s 1 day's work}} \cr & = \frac{5}{{160}} + \frac{8}{{256}} \cr & = \frac{1}{{32}} + \frac{1}{{32}} \cr & = \frac{1}{{16}} \cr} $$
Hence, 5 mens and 8 women together can complete the work in 16 days.

Efficiency of A = 3 efficiency of B
$$\left( {{\text{A}} = 3,{\text{B}} = 1} \right)$$
$$\frac{2}{5}$$ th of the work done by (A + B) in 9 days
Total work (A + B) = $$\frac{{45}}{2}$$ days will be completed
$$\eqalign{ & {\text{Total work}} \cr & = {\text{days}} \times {\text{efficiency }}\left( {{\text{A}} + {\text{B}}} \right) \cr & = \frac{{45}}{2} \times 4 \cr & = 90 \cr & {\text{Number of days for B }} \cr & {\text{ = }}\frac{{{\text{Total work}}}}{{{\text{Efficiency}}}} \cr & = \frac{{90}}{1} \cr & = 90{\text{ days}} \cr} $$

B's efficiency
= (A + B)'s efficiency - A's efficiency
= 5 - 3
= 2 pages/hour
B's time
2 pages in 1 hour
42 pages in 21 hours

A's one day work = 3 units
B's one day work = 2 units
A starts the work and does 3 units and B does the work 2 units/day.
They both do 5 units of work in 2 days.
They both do 35 units of work in 14 days
(Divide $${\frac{{36}}{5}}$$, take it to the closest)
$$\eqalign{ & {\text{Work left }} \Rightarrow 36 - 35 = 1{\text{unit}}{\text{.}} \cr & {\text{Now, A's turn}}{\text{.}} \cr & {\text{A completes}} \cr & \Rightarrow \frac{{1{\text{ unit}}}}{{{\text{3 units/day}}}} \cr & = \frac{1}{3}{\text{ day}} \cr & {\text{Whole work completes in}} \cr & \Rightarrow 14 + \frac{1}{3} \cr & = 14\frac{1}{3}{\text{ days}} \cr} $$

If labourer had come for 20 days he would have earned = 20 × 75 = Rs. 1500
If labourer had absented for 20 days he would have earned fined for = 20 × 15 = Rs. 300

$$\eqalign{ & {\text{1 men's 1 day's work}} \cr & = \frac{1}{{63 \times 18}} \cr & = \frac{1}{{1134}} \cr & {\text{1 women's 1 day's work}} \cr & = \frac{1}{{189 \times 9}} \cr & = \frac{1}{{1701}} \cr & {\text{1 children's 1 day's work}} \cr & = \frac{1}{{486 \times 7}} \cr & = \frac{1}{{3402}} \cr} $$
(4 men + 9 women + 12 children)'s 1 day's work
$$\eqalign{ & = \frac{4}{{1134}} + \frac{9}{{1701}} + \frac{{12}}{{3402}} \cr & = \frac{{42}}{{3402}} \cr & = \frac{1}{{81}} \cr} $$
Hence, 4 mens , 9 women and 12 children together will complete the work in 81 days.

$$\eqalign{ & {\text{1 men's 1 day's work}} \cr & = \frac{1}{{24 \times 16}} \cr & = \frac{1}{{384}} \cr & {\text{1 boy's 1 day's work}} \cr & = \frac{1}{{16 \times 48}} \cr & = \frac{1}{{768}} \cr & {\text{12 men's 4 day's work}} \cr & = \left( {\frac{{12}}{{384}} \times 4} \right) \cr & = \frac{1}{8} \cr & {\text{Remaining work}} \cr & = \left( {1 - \frac{1}{8}} \right) \cr & = \frac{7}{8} \cr & \left( {{\text{12 men}} + {\text{12 boy}}} \right){\text{'s 1 day's work}} \cr & = \left( {\frac{{12}}{{384}} + \frac{{12}}{{768}}} \right) \cr & = \left( {\frac{1}{{32}} + \frac{1}{{64}}} \right) \cr & = \frac{3}{{64}} \cr} $$
$$\frac{3}{{64}}$$ work is done by (12 men + 12 boy)'s in 1 day
$$\eqalign{ & \therefore \frac{7}{8}{\text{ work is done by them in }} \cr & {\text{ = }}\frac{{64}}{3} \times \frac{7}{8}{\text{ days}} \cr & = \frac{{56}}{3}{\text{ days}} \cr & = {\text{18}}\frac{2}{3}{\text{ days}} \cr} $$

$$\eqalign{ & {\text{Let 1 man's 1 day's work}} = x \cr & {\text{And }} \cr & {\text{1 women's 1 day's work}} = y \cr & {\text{Then,}} \cr & \Rightarrow 4x + 10y = \frac{1}{3} \times \frac{1}{4} = \frac{1}{{12}} \cr & \Rightarrow 4x + 10y = \frac{1}{{12}} \cr & \Rightarrow 2x + 5y = \frac{1}{{24}}.....(i) \cr & {\text{And,}} \cr & \Rightarrow 6x + 12y = \frac{1}{9} \cr & \Rightarrow 2x + 4y = \frac{1}{{27}}.....({\text{ii}}) \cr} $$
Subtracting (ii) from (i), we get
$$\eqalign{ & y = \frac{1}{{24}} - \frac{1}{{27}} = \frac{1}{{216}} \cr & {\text{Now,}} \cr} $$
Now,
(6 men + 12 women)'s 3 day's work
$$\eqalign{ & = \left( {\frac{1}{9} \times 3} \right) \cr & = \frac{1}{3} \cr & {\text{Work completed}} \cr & = \left( {\frac{1}{3} + \frac{2}{9} + \frac{1}{3}} \right) \cr & = \frac{8}{9} \cr & \therefore {\text{Remainig work}} \cr & = \left( {1 - \frac{8}{9}} \right) \cr & = \frac{1}{9} \cr & {\text{1 women's 3 day's work}} \cr & = \left( {\frac{1}{{216}} \times 3} \right) \cr & = \frac{1}{{72}} \cr} $$
In 3 day's $$\frac{1}{{72}}$$ work is done by 1 women.
$$\eqalign{ & \therefore {\text{In 3 day's }}\frac{1}{9}{\text{work is done by}} \cr & {\text{ = }}\left( {72 \times \frac{1}{9}} \right) \cr & = {\text{8 women}}{\text{.}} \cr} $$

Try these question with the help of the option to save the time
Let B takes x days to complete the work
∴ A takes (x - 5)days

Now take the option 'B' i.e x = 20days
∴ Time taken by B = 20days and A = 15days
T.W = LCM of number of day taken by A and B = 60.
Work Efficiency ration A : B = 4 : 3
∴Total Time taken to complete the work together = $$\frac{60}{4+3}$$ =   $$8\frac{4}{7}$$  days
This option not matched with $${\text{11}}\frac{1}{9}$$

Now take the option 'C' i.e x = 25days
∴ Time taken by B = 25days and A = 20days
T.W = LCM of number of day taken by A and B = 100.
Work Efficiency ration A : B = 5 : 4
∴Total Time taken to complete the work together = $$\frac{100}{5+4}$$ =   $$11\frac{1}{9}$$  days
Hence , Option (C) is the correct .