**Quantitative Aptitude Notes: Time and Work (Part - 1)**

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__Quantitative Aptitude Notes: Time and Work (Part - 2)__

__Quantitative Aptitude Notes: Time and Work (Part - 2)__

**Type 4 – Based on Efficiency**

**1. A takes twice as much time as B or thrice as much time as C to finish a piece of work. Working together, they can finish the work in 2 days. B can do the work alone in:**

**Solution:**

Then (1/x +
2/x + 3/x) = ½ => 6/x = ½ => x = 12

So, B takes
(12/2) = 6 days to finish the work

**2. A is thrice as good as workman as B and therefore is able to finish a job in 60 days less than B. Working together, they can do it in:**

**Solution:**

Ratio of
times taken by A and B = 1 : 3.

The time
difference is (i.e., 3 – 1) 2 days while B take 3 days and A takes 1 day.

If
difference of time is 2 days, B takes 3 days.

If
difference of time is 60 days, B takes (3/2 × 60) = 90 days

So A takes
30 days to do the work

A’s 1 day
work = 1/30

B’s 1 day
work = 1/90

(A + B)’s 1
day work = (1/30 + 1/90) = 4/90 = 2/45

Therefore,
A and B together can do the work in 45/2 = 22 ½ days

**3. A is 30% more efficient than B. How much time will they, working together, take to complete a job which A alone could have done in 23 days?**

**Solution:**

Ratio of
times taken by A and B = 100: 130 = 10 : 13.

Suppose B
takes x days to do the work.

Then, 10 :
13 :: 23 : x => x = (23 × 13/10) => x = 299/10

A’s 1 day
work = 1/23; B’s 1 day work = 10/299

(A + B)’s 1
day’s work = (1/23 + 10/299) = 23/299 = 1/13.

Therefore,
A and B together can complete the work in 13 days.

**4. Sakshi can do a piece of work in 20 days. Tanya is 25% more efficient than Sakshi. The number of days taken by Tanya to do the same piece of work is:**

**Solution:**

Ratio of
times taken by Sakshi and Tanya = 125: 100 = 5: 4.

Suppose Tanya
takes x days to do the work => 5: 4 :: 20: x => x = 4*20 / 5 => x = 16
days

Hence,
Tanya takes 16 days to complete the work.

**5. A works twice as fast as B. If B can complete a work in 12 days independently, the number of days in which A and B can together finish the work in:**

**Solution:**

Ratio of
rates of working of A and B = 2 : 1

So, ratio
of times taken = 1 : 2

B’s 1 day
work = 1/12

Therefore,
A’s 1 day work = 1/6; (2 times of B’s work)

(A + B)’s
1day work = (1/6 + 1/12) = 3/12 = ¼

So, A and B
together can finish the work in 4 days

**Type 5 – Based on Men or Women**

**1. If daily wages of a man is double to that of a woman, how many men should work for 25 days to earn Rs.14400? Given that wages for 40 women for 30 days are Rs.21600.**

**Solution:**

Wages of 1
woman for 1 day = 21600/(40 × 30)

Wages of 1
man for 1 day = (21600 × 2)/(40 × 30)

Wages of 1
man for 25 days = (21600 × 2× 25)/(40 × 30)

Number of
men = 14400/[(21600 × 2 × 25)/(40 × 30)] = 144/9 = 16

**2. 25 men worked together for 16 days to get a wage of Rs.11500. How many women must work together for 48 days to receive a wage of Rs.31050, if daily a woman receives half the wage of a man?**

**Solution:**

Daily wage
of a man = Rs. 11500/(25 × 16) = Rs.115/4

Daily wage
of a woman being half that of a man, it is, Rs.115/8

So to
receive Rs.31050 in 48 days, the number of women working would be=31050/(48
×115/8)=1035/23= 45

**3. Six men or ten boys can do a piece of work in fifteen days. How long would it take for 12 men and 5 boys to do the same piece of work?**

**Solution:**

6 men = 10
boys

Then, 1 boy
= 6/10 men = 3/5 men

Then, 5
boys = 3/5 × 5 = 3 men

12 men + 5
boys = 15 men

1 work done
= 6 men × 15 days

Therefore,
6 × 15 = 15 × ? days

? days = 6
× 15/15 = 6 days.

**Type 6 – Based on Group work**

**1. 9 children can complete a piece of work in 360 days. 18 men can complete the same piece of work in 72 days and 12 women can complete the piece of work in 162 days. In how many can 4 men, 12 women and 10 children together complete the piece of work?**

**Solution:**

1 child’s 1
day’s work = 1/360 ×9 = 1/3240

10
children’s 1 day’s work = 1/324

1 man’s 1
day’s work = 1/72 × 18 = 1/1296

4 men’s 1
day’s work = 1 ×4/1296 = 1/324

12 women’s
1 day’s work = 1/162 given

Then, (4
men + 12 women + 10 children)’s 1 day’s work = 1/324 + 1/162 + 1/324 = 1/324 +
2/324 + 1/324 = 4/324 = 1/81

Therefore,
the required No. of days = 81 days.

**2. 12 men can complete a piece of work in 36 days. 18 women can complete the same piece of work in 60 days. 8 men and 20 women work together for 20 days. If only women were to complete the remaining piece of work in 4 days, how many women would be required?**

**Solution:**

12 men in
36 days can do a work.

1 man in a
day can do 1/ (12×36) work.

8 men in 20
days can do 8×20/ (12×36) = 10/ 27 work.

Similarly,
we find that 20 women in 20 days can do 10/ 27 work.

Remaining
work = 7/ 27

Now, in 60
days a work is done by 20 women.

In 1 day a
work done by 20×60 women.

In 4 days
7/ 27 work is done by 20×60×7/ (27×4) = 70 women.

**3. The work done by a man, a woman and a child is in the ratio of 3 : 2 : 1. There are 20 men, 30 women and 48 children in a factory. Their weekly wages amount to Rs 840, which is divided in the ratio of work done by the men, women and children. What will be the wages of 15 men, 21 women and 30 children for 2 weeks?**

**Solution:**

Ratio of
wages of 20 men, 30 women and 48 children per week = 3*20 : 2*30 : 1*48 = 5: 5:
4

Total wages
of 20 men per week = 5/14 * 840 = Rs. 300

Therefore,
wages of a man per week = Rs. 15,

Similarly,
wages of woman per week = Rs. 10 and wages of child per week = Rs. 5

Total wages
of (15 men, 21 women and 30 children) per week = 15*15 + 21*10 + 30*5 = 585

Total wages
for 2 weeks = Rs. 1170.

**4. 8 men can complete a piece of work in 4 days. 12 women can complete the same piece of work in 4 days whereas 8 children can complete the same piece of work in 8 days. 2 men, 8 children and 3 women work together for 2 days. If only women were to finish the remaining work in 2 days, how many total women would be required?**

**Solution:**

8 men can
complete a piece of work in 4 days

=> 1 man
can complete the work in 8×4 = 32 days (because number of days is inversely
proportional to number of persons working)

=> Work
done by 1 man in 1 day = 1/32

12 women
can complete the same piece of work in 4 days

=> 1
woman can complete the work in 12×4 = 48 days

=> Work
done by 1 woman in 1 day = 1/48

8 children
can complete the same piece of work in 8 days

=> 1
child can complete the work in 8×8 = 64 days

=> Work
done by 1 child in 1 day = 1/64

Work done
by 2 men, 8 children and 3 women in 2 days =2(2×1/32+8×1/64+3×1/48) =
2(1/16+1/8+1/16)=1/2

Remaining
work = 1−1/2=1/2

Suppose n
women complete this work in 2 days.

Then,
n×1/48×2 =1/2 => n =12

**5. 8 men and 4 women together can complete a piece of work in 6 days. Work done by a man in one day is double the work done by a woman in one day. If 8 men and 4 women started working and after 2 days, 4 men left and 4 new women joined, in how many more days will the work be completed?**

**Solution:**

Let work
done by 1 man in 1 day = 2x

work done by
1 woman in 1 day = x

8 men and 4
women together can complete a piece of work in 6 days.

Work done
by 8 men and 4 women in 1 day =1/6

⇒
8×2x+4x=1/6 ⇒ 20x=1/6⇒x=1/120

8 men and 4
women worked for 2 days.

Work
completed =1/6 × 2 = 1/3

Pending
work =1−1/3=2/3

Then 4 men
left and 4 new women joined them.

i.e., 4 men
and 8 women worked and completed the work.

Work done
by 4 men and 8 women in 1 day = 4 * 2x+8 * x=16x=16/120=2/15

Required
number of days =(2/3) / (2/15) = 5

**6. The work done by women in 10 hours is equal to the work done by a man in 8 hours and by a boy in 12 hours. If working 8 hours per day 12 men can complete a work in 6 days then in how many days can 8 men, 15 women and 18 boys together finish the same work working 10 hours per day?**

**Solution:**

8M = 10W =
12B

8M + 15W +
18B ⇒ 8M + 12M +
12M ⇒ 32M

12M × 6 × 8
= 32M × ? × 10 => ? = 1 4/5 days

*Continued.....*