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

1. 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

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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).

2. 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

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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).

3. 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

4. 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

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

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