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

**CRE 5 - Man Days (single group of people) | Arithmetic - 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?

Answer: 10

**Explanation** :

Total work = Men × Days

Since total work is same in both cases.

⇒ Work done by 10 men in 8 days = Work done by 8 men in 10 days.

∴ M_{1} × D_{1} = M_{2} ×** **D_{2}

⇒ 10 × 8 = 8 × x

⇒ x = (10 × 8)/8 = 10 days.

Hence, 10.

Workspace:

**CRE 5 - Man Days (single group of people) | Arithmetic - 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

Answer: Option B

**Explanation** :

15 men can do a piece of work in 56 days.

∴ M_{1} = 15, D_{1} = 56 days

Let x be the number of men needed to do the same work in 7 days.

∴ M_{2} = x, D_{2} = 7 days

∵ Work done by 15 men in 56 days = Work done by x men in 7 days

∴ M_{1} × D_{1} = M_{2} × D_{2}

∴ 15 × 56 = x × 7

∴ x = 120 men

Hence option (b).

Workspace:

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

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

Answer: 300

**Explanation** :

When M_{1} men can complete W_{1} work in D_{1 }days while M_{2} men can complete W_{2} work in D_{2} days, then

∴ $\frac{{\mathrm{M}}_{1}{\mathrm{D}}_{1}}{{\mathrm{W}}_{1}}$ = $\frac{{\mathrm{M}}_{2}{\mathrm{D}}_{2}}{{\mathrm{W}}_{2}}$

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.

Workspace:

**CRE 5 - Man Days (single group of people) | Arithmetic - 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.

∴ $\frac{{\mathrm{M}}_{1}{\mathrm{H}}_{1}{\mathrm{D}}_{1}}{{\mathrm{W}}_{1}}$ = $\frac{{\mathrm{M}}_{2}{\mathrm{H}}_{2}{\mathrm{D}}_{2}}{{\mathrm{W}}_{2}}$

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

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

Hence, 24.

Workspace:

**CRE 5 - Man Days (single group of people) | Arithmetic - 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).

Workspace:

**CRE 5 - Man Days (single group of people) | Arithmetic - 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).

Workspace:

**CRE 5 - Man Days (single group of people) | Arithmetic - 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

Answer: Option D

**Explanation** :

Let the number of men initially be 'm'.

m men can complete the work in 20 days while (m - 10) men can complete the same work in 40 days.

∴ m × 20 = (m - 10) × 40

⇒ m = 2m - 20

⇒ m = 20

Hence, option (d)

Workspace:

**CRE 5 - Man Days (single group of people) | Arithmetic - 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**,

$\frac{{\mathrm{M}}_{1}{\mathrm{H}}_{1}}{{\mathrm{W}}_{1}}$ = $\frac{{\mathrm{M}}_{2}{\mathrm{H}}_{2}}{{\mathrm{W}}_{2}}$

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

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

Hence, option (a).

Workspace:

**CRE 5 - Man Days (single group of people) | Arithmetic - 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).

Workspace:

**CRE 5 - Man Days (single group of people) | Arithmetic - 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

Answer: Option E

**Explanation** :

Work rate = 90 women

Time = (18 × 9) hours

∴ Work done = (90 × 18 × 9) women hours

Later, work rate = 54 women

Time = (d × 6) hours (d = number of days)

Since work done is the same,

∴ 90 × 9 × 18 = 54 × 6 × d

d = 45 days

Hence, option (e).

Workspace:

**CRE 5 - Man Days (single group of people) | Arithmetic - 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

Answer: Option D

**Explanation** :

Total food available for 900 patients for 60 days = 900 × 60 units

Total food consumed by 900 patients in 40 days = 900 × 40 units

Food remaining = 900 × 20 units

Number of patients remaining = 500

∴ Number of days = 18000/500 = 36

∴ Number of extra days = 36 – 20 = 16 days

Hence, option (d).

Workspace:

**CRE 5 - Man Days (single group of people) | Arithmetic - 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

Answer: Option E

**Explanation** :

Total water available for 280 members for 180 days = 280 × 180 units

Total available consumed by 280 members in 100 days = 280 × 100 units

Water available after 100 days = 280(180 – 100) = 280 × 80 units

Number of members after 100 days = 320

∴ Number of days that the water will sufficient = 22400/320 = 70 days.

Hence, option (e).

Workspace:

**CRE 5 - Man Days (single group of people) | Arithmetic - 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).

Workspace:

**CRE 5 - Man Days (single group of people) | Arithmetic - 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

Answer: Option D

**Explanation** :

The amount of food consumed by 400 soldiers in 100 days = 10 tonnes = 10 × 1000 = 10000 kg

The amount of food consumed by 400 soldiers in 20 days = (20 × 10000)/100 = 2000 kg

The amount of food consumed by 40 soldiers in 20 days = 2000/10 = 200 kg

Hence, option (d).

Workspace:

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