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

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).

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).

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 2 women in 6 days = (5m + 2w) × 6
Work done by 7 men and 6 women in d days = (7m + 6w) × d

Since the work done is same in all these cases.

⇒ (m + 2w) × 12 = (5m + 2w) × 6 = (7m + 6w) × d

Equating first 2 expressions
⇒ (m + 2w) × 12 = (5m + 2w) × 6
⇒ 2m + 4w = 5m + 2w
⇒ 2w = 3m

Now equating last 2 expressions
⇒ (5m + 2w) × 6 = (7m + 6w) × d [Substitute 2w = 3m]
⇒ (5m + 3m) × 6 = (7m + 9m) × d
⇒ 8m × 6 = 16m × d
⇒ d = 3

Hence, 3.

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).