Practice Questions for Time & Work | CRE 5 - Man Days (single group of people)

1. CRE 5 - Man Days (single group of people) | Time & Work

If 10 men can do a piece of work in 8 days, in how many days can 8 men do the same work?

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2. CRE 5 - Man Days (single group of people) | Time & Work

15 men can do a piece of work in 56 days. How many men are needed to do the work in 7 days?

(a)
60
(b)
120
(c)
150
(d)
145
(e)
180

3. CRE 5 - Man Days (single group of people) | Time & Work

If 4 men can reap 80 hectares in 48 days, then how many hectares can 24 men reap in 30 days?

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Answer: 300

Explanation :

When M₁ men can complete W₁ work in D₁days while M₂ men can complete W₂ work in D₂ days, then

∴ $\frac{M_{1} D_{1}}{W_{1}}$ = $\frac{M_{2} D_{2}}{W_{2}}$

Now, 4 men can reap 80 hectares in 48 days, and 24 men reap 'x' hectares in 30 days.

⇒ $\frac{4 \times 48}{80}$ = $\frac{24 \times 30}{x}$

⇒ $\frac{4 \times 48}{24 \times 30}$ = $\frac{80}{x}$

⇒ x = 300

Hence, 300.

4. CRE 5 - Man Days (single group of people) | Time & Work

If 8 men can cut a number of trees in 24 days by working 6 hours a day, for how many hours a day would 3 men have to work in order to cut thrice the number of trees in 48 days?

(a)
24 hours
(b)
20 hours
(c)
16 hours
(d)
18 hours
(e)
22 hours

Answer: Option A

Explanation :

Let 8 men can cut 'x' number of trees in 24 days working 6 hours a day, while 3 men can cut '3x' number of trees in 48 days working 'h' hours per day.

∴ $\frac{M_{1} H_{1} D_{1}}{W_{1}}$ = $\frac{M_{2} H_{2} D_{2}}{W_{2}}$

⇒ $\frac{8 \times 6 \times 24}{x}$ = $\frac{3 \times h \times 48}{3 x}$

⇒ h = $\frac{8 \times 6 \times 24 \times 3}{3 \times 48}$ = 24

Hence, 24.

5. CRE 5 - Man Days (single group of people) | Time & Work

18 men can make 168 wood chairs in 10 hours. If 3 men leave the job how many chairs will be made in 8 hours?

(a)
144
(b)
132
(c)
120
(d)
112
(e)
96

Answer: Option D

Explanation :

18 men in 10 hours make 168 wood chairs i.e. work done by 18 men in 10 hours is 168.

After 3 men leave, total number of men = 18 – 3 = 15

Let 15 men make x chairs in 8 hours.

$\frac{M_{1} H_{1}}{W_{1}} = \frac{M_{2} H_{2}}{W_{2}}$

∴ $\frac{18 \times 10}{168} = \frac{15 \times 8}{x}$

∴ x = 112 chairs

Hence, option (d).

6. CRE 5 - Man Days (single group of people) | Time & Work

A certain number of men can finish a piece of work in 20 days. If however there were 10 men less it will take 20 days more for the work to be finished. How many men were there originally?

(a)
25
(b)
13
(c)
15
(d)
20
(e)
None of these

7. CRE 5 - Man Days (single group of people) | Time & Work

If 90 women working 9 hours a day can do a piece of work in 18 days, in how many days will 54 women working 6 hours a day do the same work?

(a)
15 days
(b)
24 days
(c)
30 days
(d)
36 days
(e)
45 days

8. CRE 5 - Man Days (single group of people) | Time & Work

In a hospital there is sufficient food for its 900 patients for 60 days. After 40 days, 400 patients are discharged from the hospital and no new ones are added. For how many extra days will the rest of the food last for the remaining patients if each patient consumed the same amount of food?

(a)
14 days
(b)
2 days
(c)
12 days
(d)
16 days
(e)
6 days

9. CRE 5 - Man Days (single group of people) | Time & Work

112 boys manufacture 128 toys in a day by working 8 hours; in how many days can 42 boys manufacture 210 toys by working 5 hours a day?

(a)
2
(b)
4
(c)
7
(d)
10
(e)
14

Answer: Option C

Explanation :

112 boys manufacture 128 toys in a day by working 8 hours

Let 42 boys manufacture 210 toys by working 5 hours a day, in x days

$\frac{M_{1} D_{1} H_{1}}{W_{1}} = \frac{M_{2} D_{2} H_{2}}{W_{2}}$

∴ $\frac{112 \times 1 \times 8}{128}$ = $\frac{42 \times x \times 5}{210}$

∴ 112 × 1 × 8 × 210 = 42 × x × 5 × 128

∴ x = 7 days

Hence, option (c).

10. CRE 5 - Man Days (single group of people) | Time & Work

Running at the same constant rate, 6 identical machines can produce a total of 180 bottles per hour. How many bottles could 15 such machines produce in 30 minutes?

(a)
225
(b)
300
(c)
250
(d)
350

Answer: Option A

Explanation :

6 machines can produce 180 bottles per hour

Hence, 1 machine can produce 180/6 = 30 bottles per hour and 15 bottles in 30 minutes.

∴ 15 machines can produce 15 × 15 = 225 bottles per hour.

Alternately,
$\frac{M_{1} H_{1}}{W_{1}}$ = $\frac{M_{2} H_{2}}{W_{2}}$

⇒ $\frac{6 \times 60}{180}$ = $\frac{15 \times 30}{B}$

⇒ B = $\frac{15 \times 30 \times 180}{6 \times 60}$ = 225

Hence, option (a).

11. CRE 5 - Man Days (single group of people) | Time & Work

If 10 men can dig a well in 7 days by working 12 hours a day. What is the number of men required to dig a well in 4 days by working 14 hours a day?

(a)
15
(b)
10
(c)
12
(d)
8
(e)
6

Answer: Option A

Explanation :

10 men working 6 hours a day can dig a well in 7 days.

Let x be required to dig a well in 4 days by working 14 hours a day.

$\frac{M_{1} D_{1} H_{1}}{W_{1}} = \frac{M_{2} D_{2} H_{2}}{W_{2}}$

∴ 10 × 7 × 12 = x × 4 × 14

∴ x = 15 men

Hence, option (a).

12. CRE 5 - Man Days (single group of people) | Time & Work

During a severe draught, a society of 280 members had sufficient water stored for 180 days. After 100 days 40 new members joined the society. For how many days after the 40 new members joined the society would the rest of the water be sufficient assuming everyone consumed the same amount of water?

(a)
44 days
(b)
50 days
(c)
56 days
(d)
64 days
(e)
70 days

13. CRE 5 - Man Days (single group of people) | Time & Work

If 16 men, working for 4 hrs per day for 8 days get 80/- then how many men required if the work is 6 hrs per day for 16 days they get 120/-?

(a)
9
(b)
7
(c)
6
(d)
8
(e)
10

Answer: Option D

Explanation :

Let the men required = x

We know that

Work = strength × time

∴ $\frac{m_{1} \times h_{1} \times t_{1}}{w_{1}} = \frac{m_{2} \times h_{2} \times t_{2}}{w_{2}}$

∵ Work ∝ wages

∴ $\frac{16 \times 4 \times 8}{80} = \frac{x \times 6 \times 16}{120}$

⇒ x = 8 men

Hence, option (d).

14. CRE 5 - Man Days (single group of people) | Time & Work

If 400 soldiers eat 20 tonnes of food in 100 days, how much will 40 soldiers eat in 20 days?

(a)
1 ton
(b)
10 kg
(c)
100 kg
(d)
200 kg

CRE 5 - Man Days (single group of people) | Time & Work

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