CGL MAINS 2015 : Quant Quiz

1.A merchant purchases a wrist watch for Rs. 450 and fixes its list price in such a way that after allowing a discount of 10%, he earns a profit of 20%. Then the list price (in rupees) of the wrist watch is. 

(1) 500 

(2) 600 

(3) 750 

(4) 800 

2.The simple and compound interests on a sum of money for 2 years are Rs. 8400 and Rs. 8652 respectively. The rate of interest per annum is 

(1) 6%  

(2) 7.5%  

(3) 9%  

(4) 4.5% 

3.A can complete a piece of work in 12 days.  B is  60% more efficient than A. the number of days that B  will take to complete the same work is 

(1) 6 

(2) 7 1/2

(3) 8 

(4) 8 1/2 

4.Two pipes can fill an empty tank separately in 24 minutes and 40 minutes respectively and a third pipe can empty 30 gallons of water per minute. If all the three pipes are open, empty tank becomes full in one hour. The capacity of the tank (in gallons) is 

(1) 800 

(2) 600 

(3) 500 

(4) 400

5.A dealer marks his goods 30% above his cost price and then allows 15% discount on it. What is the cost price of an article on which he gains Rs. 84? 

(1) Rs. 800 

(2) Rs. 560 

(3) Rs. 373.33 

(4) Rs. 280

6.A shopkeeper wishes to give 5% commission on the marked price of an article but also wants to earn a profit of 10%. If his cost price is Rs. 95. Then the marked price is

(1) Rs. 100 

(2) Rs. 110 

(3) Rs. 120 

(4) Rs. 130

7.A and B enter into partnership with capitals in the ratio 5 : 6. At the end of 8 months A wirhdraws  his capital. They received profits in the ratio 5 :9. B invested the capital for 

(1) 6 months 

(2) 8 months 

(3) 10 months 

(4) 12 months 

8.The number of coins, each of radius 0.75 cm and thickness  0.2 cm, to be melted to make a right circular cylinder of height 8 cm and radius 3 cm, is 

(1) 640 

(2)  600 

(3) 500 

(4) 480

9.If A travels to his school from his house at the speed of 3 km/hr then he  reaches the school 5 minutes late. If he travels at the speed of 4 km/hr, he reaches the school 5 minutes earlier than school time. The distance of his school from his house is 

(1)  1 km  

(2) 2 km 

(3) 3 km 

(4) 4 km 

10.A train travelling with a speed of 60 km/hr catches another train travelling in the same direction and then leaves it 120 m behind in 18 seconds. The speed  of the second train is 

(1)26 km/hr 

(2) 35 km/hr 

(3) 36 km/hr 

(4) 63 km/hr 

ANSWERS AND SOLUTION :
1.(2) If the marked price of the wrist watch be Rs. x, then
x * 90/100 = (450 * 120)/100 = 540
=> x = (540 * 100)/90 = Rs. 600

2.(1) Difference = Rs.(8652 – 8400)
= Rs. 252
so Rate = (2 * Difference)/S.I * 100
= (2 * (252/8400) * 100 = 6%

3.(2) Ratio of their efficiency
= 100 : 160 = 5 : 8
so Ratio of time taken = 8 : 5
so Time taken by B
= 12 * 5/8 = 15/2 = 7 1/2 days
 
4.(2) Capacity of the tank = x gallons.
so Part of the tank filled in 1 minute
= x/24 + x/40 – 30
so 60 (x/24 + x/40 – 30)  = x
so x/24 + x/40 – x/60 = 30
=> (5x + 3x – 2x)/120 = 30
=> x/20 = 30
x = 600 gallons
 
5.(1)
CP of article = Rs. x
so Marked price = 130x/100 = Rs. 13x/100
so S.P.
= 13x/10 * 85/100 = Rs. 221x/200
so 221x/200 – x = 84 => 21x/200 = 84
=> x = (84 * 200)/21 = Rs.  800
 
6.(2) Marked price = Rs. x. then.
(x * 95)/100 = (95 * 110)/100
=> x = Rs. 110

7.(4) If b invested for y months, then
(5* 8)/(6 * y) = 5/9
=> y = 12 months

8.(1) volume of the cylinder = πr^2 h
= π × (3)^2  ×8 = 72 πcm^3
Volume of one coin
= π×(0.75)^2 ×0.2
so Number of coins
= 72π/(π ×0.75 × 0.75 ×0.2) = 640

9.(2) If the distance between the school and home be x km. then
x/3 – x/4 = 10/60
=> x/12 = 1/6
x = 1/6 * 12 = 2 km

10.(3) 60 kmph = (60 * 5)/18 m/sec
= 50/3 m/sec
If the speed of second train be x m/sec, then
50/3 – x = 120/18 = 20/3
x = 50/3 – 20/3 = 10 m/sec
= (10 * 18/5) kmph
= 36 kmph