# CRE 6 - Man Days (multiple groups of people) | Arithmetic - Time & Work

**CRE 6 - Man Days (multiple groups of people) | Arithmetic - Time & Work**

If 28 men and 44 women can do a piece of work in 10 days, in how many days can the work be done by 7 men and 11 women working together?

- (a)
28

- (b)
32

- (c)
40

- (d)
42

- (e)
Can't be determined

Answer: Option C

**Explanation** :

28 men and 44 women can do a piece of work in 10 days.

If m and w are the number of days taken by a man and a woman to finish the work,

Then,

$\frac{28}{m}+\frac{44}{w}=\frac{1}{10}$

∴ $\frac{7}{m}+\frac{11}{w}=\frac{1}{40}$

∴ 7 men and 11 women can finish the work in 40 days.

Hence, option (c).

**Video Solution**:

Workspace:

**CRE 6 - Man Days (multiple groups of people) | Arithmetic - Time & Work**

A man, a woman, and a child can do a piece of work in 12 days. Man only can do it in 48 days. Woman can do it in 32 days and in how many days child can do the same work?

- (a)
24

- (b)
80

- (c)
32

- (d)
16

- (e)
14

Answer: Option C

**Explanation** :

Let the amount of work to be done = LCM (12, 48, 32) = 96 units.

∴ Efficiency of a man = 96/48 = 2 units/day

Efficiency of a woman = 96/32 = 3 units/day

Let the efficiency of a boy = 'b' units/day

A man, a woman, and a child can do a piece of work in 12 days.

⇒ 96 = (2 + 3 + b) × 12

⇒ 8 = 2 + 3 + b

⇒ b = 3

∴ Efficiency of a boy = 3 units/day

⇒ Time taken by a boy to complete the work alone = 96/3 = 32 days.

**Alternately**,

Say the child takes C days to complete the work.

Amount of work all together can do in one day = $\frac{1}{12}$ of total work.

Amount of work Man can do in one day = $\frac{1}{48}$ of total work

Amount of work Woman can do in one day = $\frac{1}{32}$ of total work

Amount of work Child can do in one day = $\frac{1}{C}$ of total work.

According to question:

⇒ $\frac{1}{48}$ + $\frac{1}{32}$ + $\frac{1}{C}$ = $\frac{1}{12}$

⇒ $\frac{1}{C}$ = $\frac{1}{12}$- $\frac{1}{48}$ - $\frac{1}{32}$ = $\frac{1}{32}$

⇒ C = 32 days.

Hence, option (c).

**Video Solution**:

Workspace:

**CRE 6 - Man Days (multiple groups of people) | Arithmetic - Time & Work**

One man two women can complete a task in 12 days, while 5 men and 3 women can complete the same task in 6 days. How many days will it take 13 men and 5 women to complete the same task?

- (a)
5

- (b)
4

- (c)
3

- (d)
2

- (e)
None of these

Answer: Option C

**Explanation** :

Let the efficiency of man be 'm' units/day and that of a woman be 'w' units/day

Work done by a man and two women in 12 days = (m + 2w) × 12

Work done by 5 men and 3 women in 6 days = (5m + 3w) × 6

Work done by 13 men and 5 women in d days = (13m + 5w) × d

Since the work done is same in all these cases.

⇒ (m + 2w) × 12 = (5m + 3w) × 6 = (13m + 5w) × d

Equating first 2 expressions

⇒ (m + 2w) × 12 = (5m + 3w) × 6

⇒ 2m + 4w = 5m + 3w

⇒ w = 3m

Now equating last 2 expressions

⇒ (5m + 3w) × 6 = (13m + 5w) × d [Substitute 2w = 3m]

⇒ (5m + 9m) × 6 = (13m + 15m) × d

⇒ 14m × 6 = 28m × d

⇒ d = 3

Hence, 3.

Workspace:

**CRE 6 - Man Days (multiple groups of people) | Arithmetic - Time & Work**

20 men can complete a task in 3 days, 10 women can complete the same task in 4 days while 60 boys can complete the same task in 2 days. How long will it take for 2 men, 2 women and 5 boys to complete the task together.

- (a)
16

- (b)
8

- (c)
10

- (d)
15

- (e)
None of these

Answer: Option B

**Explanation** :

20 men can complete a task in 3 days, 10 women can complete the same task in 4 days while 60 boys can complete the same task in 2 days. How long will it take for 2 men, 2 women and 5 boys to complete the task together.

Let the efficiency of a man be 'm' units/day, that of a woman be 'w' units/day and that of a boy be 'b' units/day.

20 men can complete the task in 3 days ⇒ Work done = 20m × 3 = 60m ...(1)

10 women can complete the task in 4 days ⇒ Work done = 10w × 4 = 40w ...(2)

60 boys can complete the task in 2 days ⇒ Work done = 60b × 2 = 120b ...(3)

Since work done is same in all these cases

⇒ 60m = 40w = 120b

⇒ 3m = 2w = 6b ...(4)

Let 2 men, 2 women and 5 boys complete the task in d days ⇒ Work done = (2m + 2w + 5b) × d ...(5)

Now, (5) = (3)

⇒ (2m + 2w + 5b) × d = 120b

⇒ (4b + 6b + 5b) × d = 120b [from (4)]

⇒ 15b × d = 120b

⇒ d = 8 days.

Hence, option (b).

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