1. A person started his journey in the morning. At 11 A.M, he covered 3/8 th of his journey and on the same day at 4 : 30 P.M, he covered 5/6 th of his journey. At what time did he start his journey?
a)6:00 AM
b)3:30 AM
c)6:30 AM
d)7:00 AM
2.A person increases his speed by 10 Km/hr and reaches 2 hours earlier. If he decreases his speed by 5 Km/hr, then he will reach 3 hours late. Find the speed and distance.
a) 12 km/hr, 50 Km
b)12.5 km/hr, 56.25 Km
c)10 km/hr, 50 Km
d)11.5 km/hr, 56.25 Km
3.A man takes 80 days to complete a job. Four men, 8 women and 4 machines take 5 days to complete the job. Four men, 1 woman and 2 machines take 10 days to complete the job. Find the time taken by a woman to complete the job (in days).
a)90
b)100
c)105
d)120
4.A person sold an article at a profit of 12%. If he had sold it for Rs 3.60 more, he would have gained 18%. Find the cost price.
a)60
b)55
c)65
d)70
5.24 men can complete a work in 16 days. 32 women can complete the same work in 24 days. 16 men and 16 women started working and worked for 12 days.How much part of work is now left to complete?
a)11/24
b)5/24
c)1/3
d)None of these
6.Mohan makes a profit of X%, by selling a pen for Rs 24. Had the cost price and the selling price been interchanged, it would have led to a loss of 62.5% of X. With the latter Cost Price, what should be the new selling price to get a profit of X%?
a)Rs 36.50
b)Rs 38.40
c)Rs 39.30
d)Rs 38.20
7.A boy starts to paint a fence on one day. On the second day, two more boys join him. On the third day, three more boys join the group, on the fourth day, four more boys join the group and so on. If the fence is completely painted this way in exactly 20 days, then find the number of days in which 10 men painting together can paint the fence completely. Given that every man can paint twice as fast as a boy can.
a)78
b)76
c)75
d)77
8.Two pipes can fill a tank in 20 hours and 24 hours respectively. A third pipe can empty the tank in 40 hours. If all the three are opened and function simultaneously. Then, in how much time, will the tank be full?
a)10 hrs
b)12 hrs
c)14 hrs
d)15 hrs
9.Three numbers are in the ratio 3 : 4 : 5 and their LCM is 2400. Their HCF is
a)40
b)80
c)120
d)200
10.A, B and C start at the same time in the same direction to run around a circular stadium. A completes a round in 252 seconds, B in 308 seconds and C in 198 seconds, all starting at the same point. After what time will they meet again at the starting point?
a)26 minutes 18 seconds
b)42 minutes 36 seconds
c)45 minutes
d)46 minutes 12 seconds
Answers
1.c.
In 5 1/2 hours, the man covers (5/6 - 3/8)th of his journey.
Let the total distance be x.
So, in 11/2 hours, the man covers a distance of 11x/24 Km
Speed = Distance/Time = (11x/24)/(11/2) = x/12 Km/hr
Now, we have to find the time taken by the man to cover, 3/8th of his journey
Time = 3x/8 x 12/x = 4 1/2 hours
Hence, the man started his journey at 6 : 30 A.M
2.b
Let D be the distance and S be the speed.
D/S - D/(S + 10) = 2.....(1)
D/(S-5) - D/S = 3........(2)
D x 10/S(S + 10) = 2......(i)
D x 5/S(S - 5) = 3.......(ii)
(i)/(ii)
(S - 5)/(S + 10) = 1/3
3S - 15 = S + 10
2S = 25
S = 12.5 Km/hr
D = 2 x 12.5 x 22.5/10 = 56.25 Km.
3.d
1 man can do a job in 80 days
4 man can do a job in 20 days
Let the time taken by a woman be W and that by a machine be M
1/20 + 8/W + 4/M = 1/5
1/20 + 1/W + 2/M = 1/10
Assuming 1/W = X and 1/M = Y
8X + 4Y = 3/20.....(1)
X + 2Y = 1/20....(2)
Solving 1 and 2, we get, X = 1/120
Hence W = 120 days
4.a
Let the cost price of the article be x
112x/100 + 3.60 = 118x/100
6x/100 = 3.60
x = 60 Rs
5.d
Work done by 16 men in 12 days = (16 x 12)/(16 x 24) = 1/2
Work done by 16 woman in 12 days =(16 x 12)/(32 x 24) = 1/4
Total work completed = 1/2 + 1/4 = 3/4
Remaining work = 1 - 3/4 = 1/4
6.b
Let the CP of the Pen be S
sp = 24 given
Profit = X = (24 - S)/S x 100....(1)
Now the CP and SP of the Pen is interchanged
New CP = 24
New SP = S
Loss = (24 -S)/24 x 100
Given that, loss = 62.5% of X = 62.5 x (24 - S)/S... (Substituting the value of X from 1)
This implies, (24 - S)/24 x 100 = 62.5 x (24 - S) / S
Solving, we get S = 15
Now, we have to find the value of X
Substitute X in (1)
We get X = 9/15 x 100 = 60%
With CP = 24, and profit % = 60
The SP should be 24 x 160/100 = Rs 38.40
7.d
Total number of days taken by a boy = 1 + (1 + 2) + (1 + 2 + 3) + ..... + (1 + 2 + 3 + ... + 20)
Total number of days taken by a boy = 1/6 x 20 x 21 x 22 = 1540
As efficiency of a man is double that of a boy, the number of days taken will be, 1540/2 = 770
1 man =====> 770 days
10 men =====> 77 days
8.d
The total time taken by the three pipes will be 1/20 + 1/24 - 1/40 = 8/120 = 1/15 =15 hrs
9.a
Let the numbers be 3x , 4x and 5x
lcm of these three numbers = 60x
60x = 2400
x = 40
The numbers are (3 x 40), (4 x 40), (5 x 40)
Hence hcf = 40
10.d
LCM of 252, 308 and 189 = 2772 seconds
2772 sec = 46 min 12 sec
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