1. A group of men decided to do a job in 4 days. But since 20 men dropped out every day, the job completed at the end of the 7^{th} day. How many men were there at the beginning?

a) 240

b) 280

c) 140

d) 150

Explanation: Let X be the initial number of men -:

4X = X + (X - 20) + (X - 40) + (X - 60) + (X - 80) + (X - 100) + (X - 120)

⇒ 4X = 7X - 420

⇒ 3X = 420

⇒ X = $$\frac{{420}}{3}$$

⇒ X = 140 men

2. Two typist of varying skills can do a job in 6 minutes if they work together. If the first typist typed alone for 4 minutes and then the second typist typed alone for 6 minutes, they would be left with $$\frac{1}{5}$$ of the whole work. How many minutes would it take the slower typist to complete the typing job working alone ?

a) 10 minutes

b) 15 minutes

c) 12 minutes

d) 17 minutes

Explanation: Working efficiency of both typist together,

= $$\frac{{100}}{6}$$ = 16.66% per minute

Now, let work efficiency of first typist be x and then second typist will be (16.66 - x)

First typist typed alone for 4 minutes and second typed alone for 6 minutes and they left with $$\frac{1}{5}$$ (i.e 20%) of job, means they have completed 80% job

First Typist typed in 4 minute + Second typed in 6 minutes = 80%

4 × x + 6 × (16.66 - x) = 80%

4x + 100% - 6x = 80%

x = 10%

First Typist typed 10% per minutes. Then second typed (16.66 - 10) = 6.66% per minute

Then, Second typist complete the whole job in $$\frac{{100}}{{6.66}}$$ = 15.01 = 15 minutes.

3. Two persons having different productivity of labour, working together can reap a field in 2 days. If one-third of the field was reaped by the first man and rest by the other one working alternatively took 4 days. How long did it take for the faster person to reap the whole field working alone?

a) 3

b) 6

c) 8

d) 12

Explanation: Total efficiency of two persons = 50% [As they complete work in 2 days]

First Person completes work = $$\frac{1}{3}$$ = 33.33% [In 2 days]

Rest work will be completed by Second man = $$\frac{2}{3}$$ = 66.66% [In 2 days]

So, efficiency of second person is greater.

Efficiency of second person = $$\frac{{66.66}}{2}$$ = 33.33% per day

Then, Second person will complete whole work in,

= $$\frac{{100}}{{33.33}}$$ = 3 days.

4. If m men can do a work in r days, then the number of days taken by (m + n) men to do it is :

a) $$\frac{{{\text{m}} + {\text{n}}}}{{{\text{mn}}}}$$

b) $$\frac{{{\text{r}}\left( {{\text{m}} + {\text{n}}} \right)}}{{{\text{mn}}}}$$

c) $$\frac{{{\text{m}} + {\text{n}}}}{{{\text{mr}}}}$$

d) $$\frac{{{\text{mr}}}}{{{\text{m}} + {\text{n}}}}$$

Explanation: M

_{1}× D

_{1}= M

_{2}× D

_{2}

mr = (m +n) × D

_{2}

D

_{2}= $$\frac{{{\text{mr}}}}{{{\text{m}} + {\text{n}}}}$$

5. If 10 persons can do a job in 20 days, then 20 person with twice the efficiency can do the same job in:

a) 5 days

b) 40 days

c) 10 days

d) 20 days

Explanation: By work equivalence method,

man × days × work = MAN × DAYS × WORK

10 × 20 × 1 = 20 × 2 × x

→ x = 5 days

6. If 2 men or 3 women or 4 boys can do a piece of work in 52 days, then the same piece of work will be done by 1 man, 1 woman and 1 boy in:

a) 48 days

b) 36 days

c) 45 days

d) 50 days

Explanation: Work done by 2 men = 3 women = 4 boys

1 man = 2 boys

1 woman = $$\frac{4}{3}$$ boys

Boys × days = 4 × 52 boys × days

1 man + 1 women + 1 boys,

$$ = 2 + \frac{4}{3} + 1$$

$$ = \frac{{13}}{3}$$ boys

Using work equivalent method,

boys × day = BOYS × DAYS

$$4 \times 52 = \frac{{13}}{3} \times {\text{x}}\,{\text{(let)}}$$

x = 48 days

7. Two men and women are entrusted with a task. The second man needs three hours more to cope up with the job than the second man and the woman would need working together. The first man, working alone, would need as much time as second man and the woman working together. The first man working alone, would spend eight hours less than the double period of the time second man would spend working alone. How much time would the two men and the women need to complete the task if they all asked together?

a) 2 hours

b) 1 hour

c) 3 hours

d) 4 hours

Explanation: Difference in times required by the first man (A) and second man (B) = 3 hours. Also, if t

_{a}and t

_{b}are the respective times, then

t

_{b}- t

_{a}= 3 . . . . . . . . . ..(1)

Also, B alone be take = (t

_{a}+ 3) h

2t

_{b}- t

_{a}= 8

2 × (t

_{a}+ 3) - t

_{a}= 8 [Using equation (1)]

t

_{a}= 2 hours.

Now B and woman together take 2 hours and A also take 2 hours, so time required will be half when all 3 work together. So in 1 hour work would be completed.

8. If 3 men or 4 women can plough a field in 43 days, how long will 7 men and 5 women take to plough it?

a) 10 days

b) 11 days

c) 9 days

d) 12 days

Explanation: 3 men or 4 women can plough the field in 43 days

3 men = 4 women

1 man = $$\frac{4}{3}$$ women

7 man = $$\frac{{28}}{3}$$ women

7 men and 5 women = $$5 + \frac{{28}}{3}$$ = $$\frac{{43}}{3}$$ women

4 women can plough field in 43 days

So, 1 women can plough in = 43 × 4 days

$$\frac{{43}}{3}$$ women can plough = $$\frac{{43 \times 4 \times 3}}{{43}}$$ = 12 days

9. Raj can do a piece of work in 20 days. He started the work and left after some days, when 25% work was done. After it Abhijit joined and completed it working for 10 days. In how many days Raj and Abhijit can do the complete work, working together?

a) 8

b) 6

c) 10

d) 12

Explanation: Efficiency of Raj = $$\frac{{100}}{{20}}$$ = 5%

Work completed by Raj = 25%

Rest work = 75%

Efficiency of Abhijit = $$\frac{{75}}{{10}}$$ = 7.5%

Combined efficiency = 5 + 7.5 = 12.5%

They will complete the whole work by working together in,

= $$\frac{{100}}{{12.5}}$$ = 8 days

10. If one pipe A can fill a tank in 20 minutes, then 5 pipes, each of 20% efficiency of A, can fill the tank in:

a) 80 min

b) 100 min

c) 20 min

d) 25 min

Explanation: Efficiency of pipe A,

$$\frac{{100}}{{20}}$$ = 5%

20% of efficiency of A = 1%

Then, efficiency of 5 such pipes = 5%.

Time taken to fill the tank = $$\frac{{100}}{5}$$ = 20 min.