Q.1 Carpenter A can make chair in 6hrs , Carpenter B in 7 hrs & Carpenter C in 8hrs. If each carpenter works for 8hrs per day, how many chairs will be made in 21 days ?

A) 73

B) 69

C) 61

D) 67

Ans. A

A can make in 21 days= 21*8/6 = 28 chairs

B can make in 21 days = 21*8/7 = 28chairs

C can make in 21 days=21*8/8 = 21 chairs

Therefore total no. of chairs = 28+24+21 = 73chairs

Q.2 A & B can complete work together in 5 days. If A works at twice his speed & B at half of his speed , this work can be finished in 4 days. How many days would it take for A alone to complete the job ?

A) 10

B) 15

C) 12

D) 18

Ans. A

Let A can do work in x days & B can do in y days

Thus,

1/x + 1/y = 1/5—i

2/x + 1/2y = ¼—ii

Now solve these two equations, we will get

2/x + 1/2y=1/4

4/x + 1/y=1/2

1/y=1/2 -4/x—–iii

Put the value of 1/y in eq-i

1/x+1/y = 1/5

1/x + ½-4/x = 1/5

1/x-4/x=1/5-1/2

=2-5/10 =-3/10

Thus on solving we get,

X=10

Q.3 Amit & Saurabh can complete a piece of work in 15 days. If B alone takes 20 days to complete that work. Find the time taken by A alone to complete that work .

A) 60 days

B) 61 days

C) 62 days

D) 63 days

Ans. A

Shortcut:

Xy / y-x

15*20 / 20-15 = 60 days

Q.4 20 men can complete the work in 40 days. When should 4 men leave so that the work may be finished in 48 days ?

A) 8 days

B) 10 days

C) 4 days

D) 6 days

Ans. A

Suppose 4 men leave after x days

Therefore, work done by 20 men in x days = x/40

Remaining work = 1- x/40

40-x / 40

No. of remaining days = 48-x

No. of remaining men = 20-4 = 16

If 20 men can do in 40 days 1 work

Therefore, 1 men can do in 1 day

= 1 / 20*40

16 men can do in 48-x days = 1*16*(48-x) / 20*40

Therefore, 16*(48-x) / 20*40 = 40-x / 40

192-4x = 200-5x

X=8

Q.5 25 Men were employed to do a piece of work which they could finish in 20 days but the men dropped off by 5 at the end of every 10 days. In what time will the work be completed ?

A) 23 ½ days

B) 8 days

C) 26 days

D) 17 days

Ans. A

Work done by 25 men in 1 day = 1/20

Therefore, work done by 25 men in 10 days = 1/20 * 10 = ½

Therefore, no. of workers available after 10 days

= 25-5 = 20

Work done by 25 men in 1 day = 1/20

Work done by 1 man in 1 day = 1 / 20*25

Work done by 20 men in 10 days = 1/20 * 1/25 * 20 * 10

=2/5

Again, the no. of workers available after 20 days = 20-5 = 15

Remaining work = 1 – ½ – 2/5 = 1/10

Therefore, 1/20 work is done by 25 men in 1 day

1 work is done by 1 men in = 1*20*25

1/10 work is done by 15 men in = 1*20*25*1 / 15*10 = 10/3

Therefore, total no. of days = 10+10+ 3 1/3

=23 1/3