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
