Ratio, Proportion and Partnership
- Ratio, Proportion & Partnership
- CRE 1 - Ratio
- CRE 2 - Proportion
- CRE 3 - Partnership
- PE 1 - Ratio
Percentage, Profit & Loss
- Percentage
- Profit & Loss
- CRE 1 - Percentage
- CRE 2 - Percentage Change
- CRE 3 - Successive Percentage Change
- CRE 4 - Profit & Loss
- CRE 5 - Discount
- PE 1 - Percentage
Simple and Compound Interest
- Simple & Compound Interest
- CRE 1 - Simple Interest
- CRE 2 - Compound Interest
Average, Mixture & Alligation
- Average
- Mixture & Alligation
- CRE 1 - Simple Average
- CRE 2 - Numbers Added/Removed
- CRE 3 - Weighted Average
- PE 1 - Average
- PE 2 - Average
Time and Work
- Time and Work
- CRE 1 - Basics
- CRE 2 - Working in Shifts
- CRE 3 - Payments
- CRE 4 - Man Days (single group of people)
- CRE 5 - Man Days (multiple groups of people)
- CRE 6 - Pipes & Cisterns
- PE 1 - Time and Work
Time, Speed and Distance
- Time, Speed and Distance
- CRE 1 - Basics
- CRE 2 - Relative Speed
- CRE 3 - Trains
- CRE 4 - Boats & Streams
Numbers
- CRE 1 - Simplification
- PE 1 - LCM & HCF
- PE 2 - LCM & HCF
- PE 3 - Unit's Digit
Indices & Surds
- CRE 1 - Indices
- CRE 2 - Surds
Linear & Quadratic Equations
Permutations, Combinations & Probability
Geometry, Mensuration & Trigonometry
- Geometry Basics
- CRE 1 - Geometry Basics
- CRE 2 - Triangles
- CRE 3 - Circles
- CRE 4 - Mensuration
- CRE 5 - Trigonometry
Data Interpretation
- CRE 1 - Tables
Arrangements, Ranking & Ordering
- PE 1 - Arrangements
- PE 2 - Ranking
- PE 3 - Ordering
Analogy & Odd One Out
- PE 1 - Word Analogy
- PE 2 - Word Analogy
- PE 3 - Alphabet Analogy
- PE 4 - Numbers Analogy
- PE 5 - Odd One Out
Number & Alphabet Series
- PE 1 - Number Series
- PE 2 - Alphabet Series
Coding & Decoding
- PE 1 - Coding & Decoding
Clocks & Calendars
- PE 1 - Clocks
- PE 2 - Calendars
Venn Diagram
- CRE 1 - Venn Diagram
- CRE 2 - Venn Diagram
progression
Mathematical Operations
- PE 1 - Mathematical Operations
Dice & Cubes
- PE 1 - Dice
Visual Reasoning
Blood Relation & Direction Sense
- PE 1 - Blood Relation
- PE 2 - Direction Sense
General Knowledge & Current Affairs
Syllogisms

CRE 5 - Man Days (multiple groups of people) | Time and Work

1. CRE 5 - Man Days (multiple groups of people) | Time and 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:

2. CRE 5 - Man Days (multiple groups of people) | Time and 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:

3. CRE 5 - Man Days (multiple groups of people) | Time and 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 7 men and 6 women to complete the same task?

A.
5
B.
4
C.
3
D.
2
E.
None of these

4. CRE 5 - Man Days (multiple groups of people) | Time and 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 5 - Man Days (multiple groups of people) | Time and Work

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