Time And Work - Aptitude MCQ Questions and Solutions with Explanations

Understanding the Problem:
Imagine digging a pond. It takes a certain amount of effort. That effort is made up of the number of workers, the number of hours they work each day, and the number of days they work.

What we know:
30 men working 8 hours a day take 16 days to dig the pond.

What we want to find:
How many hours a day will 32 men need to work to dig the *same* pond in 20 days?

Think of it like this:
The total work is the same (digging the same pond). Total work is calculated as: (Number of men) x (Hours per day) x (Number of days).

Let's calculate the total work:
Total work = 30 men x 8 hours/day x 16 days = 3840 man-hours

Now, let's use the total work to find the hours needed for 32 men working for 20 days:
3840 man-hours = 32 men x (Hours per day) x 20 days

Solve for "Hours per day":
(Hours per day) = 3840 man-hours / (32 men x 20 days)
(Hours per day) = 3840 / 640 = 6 hours/day

Therefore, the answer is:
A: 6 hours/day

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Alternative Solution
8 × 30 × 16 = 32 × 20 × $$x$$
$$x$$ = 6 hours per day

$$\eqalign{ & 25 \times 16 = 25 \times 4 + 30 \times x \cr & \left( {{M_1} \times {D_1}} \right) = \left( {{M_1}{D_1} \times {M_2}{D_2}} \right) \cr & 400 = 100 + 30x \cr & 300 = 30x \cr & x = 10{\text{ days}} \cr} $$

2 days → 4 + 3 = 7 units
12 days → 42 units
13 days → 42 + 4 = 46 units
Total time taken = $$13\frac{2}{3}{\text{ days}}$$

$$\eqalign{ & \left( {3m + 8w} \right) \times \frac{{75}}{8} = \left( {9m + 12w} \right) \times \frac{{25}}{7} \cr & 63m + 168w = 72m + 96w \cr & 72w = 9m \cr & \frac{m}{w} = \frac{8}{1} \cr & {\text{Total work}} = \left( {3m + 8w} \right) \times \frac{{75}}{8} \cr & = \left( {3 \times 8 + 8 \times 1} \right) \times \frac{{75}}{8} \cr & = 4 \times 75 \cr & {\text{Time taken by }}15w = \frac{{4 \times 75}}{{15 \times 1}} = 20{\text{ day}} \cr} $$

27 × 8 × 12 = 18 × 9 × x
x = 16 days

Total work of (A + B) in 4 days = 4(4 + 5) = 36
Remaining work = 100 - 36 = 64
A = $$\frac{{64}}{4}$$ = 16 days
Total days = 4 + 16 = 20 days

Efficiency of Q = 2
So, required answer = $$\frac{{36 \times \frac{2}{3}}}{2}$$  = 12 days

$$\eqalign{ & 45\% = \frac{9}{{20}} \cr & {\text{Efficiency A}} = 29{\text{ and B}} = 20 \cr & 58 \times 49 + 29 \times 20 = 3422 \cr & {\text{Required answer A}} = \frac{{3422}}{{29}} = 118\,{\text{days}} \cr} $$

Total work = 30 × 20 = 600
After 10 days = 20 × 10 = 200
Remaining work = 600 - 200 = 400
4 men left, remaining = 16 men
16 × D = 400
D = $$\frac{{400}}{{16}}$$
D = 25 days
Total days = 25 + 10 = 35 days