Mission CGL Mains 2015 : Quant Quiz

1.A man travelled a certain distance by train at the rate of 25 kmph. and walked back at the rate of 4 kmph. If the whole journey took 5 hours 48 minutes, the distance was
(1) 25 km
(2) 30 km
(3) 20 km
(4) 15 km

2.The HCF of two numbers is 23 and the other two factors of their LCM are 13 and 14. The larger of two numbers is :
(1) 276
(2) 299
(3) 345
(4) 322
3.Out of 450 students of a school 325 play football, 175 play cricket and 50 neither play football nor cricket. How many students play both football and cricket?
(1) 50
(2) 100
(3) 75
(4) 225
4.A cistern 6 m long and 4 m wide. Contains water up to a depth of 1 m 25 cm. The total area of the wet surface is
(1) 55 m^2
(2) 53.5 m^2
(3) 50 m^2
(4) 49 m^2
5.Two trains of equal length take 10 seconds and 15 seconds respectively to cross a telegraph post. If the length of each train be 120 metres, in what time (in seconds) will they cross each other travelling in opposite direction?
(1) 16
(2) 15
(3) 12
(4) 10
6.A starts from a place P to go to a place Q. At the same time B starts from Q to P. If after meeting each other A and B took 4 and 9 hours more respectively to reach their destinations, the ratio of their speeds is
(1) 3 : 2
(2) 5 : 2
(3) 9 : 4
(4) 9 : 13
7.A man can row at 5 kmph. In still water. If the velocity of current is 1 kmph. and it takes him 1 hour to row to a place and come back, how far is the place?
(1) 2.5 km
(2) 3 km
(3) 2.4 km
(4) 3.6 km
8.A trader marked his goods at 20% above the cost price. He sold half the stock at the marked price, one quarter at a discount of 20% on the marked price and the rest at a discount of 40% on the marked price. His total gain is
(1) 2%
(2) 4.5%
(3) 13.5%
(4) 15%
9. The HCF of two numbers is 15 and their LCM is 300. If one of the number is 60,the other is :
(1) 50
(2) 75
(3) 65
(4) 100
10.In a family of 8 adults and some minors, the average consumption of rice per head per month is 10.8 kg; while the average consumption for adults is 15 kg per head and for  and for minors it is 6 kg per head. The number of minors in the family is :
(1) 8
(2) 6
(3) 7
(4) 9

Answer and Solution:
1.(3)
Let the distance be x km.
Total time = 5 hours 48 minutes = 29/5 hours
so x/25 + x/4 = 29/5
=> x = 20 km

2.(4) Let the numbers be 23x and 23y where x and y are co-prime
So LCM = 23xy
As given,
23xy = 23*13*14
so x = 13, y = 14
so The largest number = 23y= 23*14 = 322

3.(2)
4.(4)Required total area = Area of four walls + area of base
= 2*1.25(6+4)+6*4
= 49m^2

5.(3)
When a train crosses a telegraph post,If covers its own length.
so Speed of first train = 120/10 = 12 m/s
Speed of second train = 120/15 = 8 m/s
Relative speed 12+8 = 20 m/s
Required time = 2*120/20 = 12 seconds

6.(1)
7.(3)Let the distance be x km.
Speed upstream = 5-1 = 4 kmph
Speed downstrean = 5+1 = 6 kmph
so x/6 + x/4 = 1
x = 2.4 km

8.(1)
9.(2)
10.(3)
Let number of minors be x.
According to the question,
(8*15+x*6)/(8+x) = 10.8
=> x = 7

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