CGL MAINS 2015 : Quant Quiz

1.The average age of four boys. five years ago was 9 years. On including a new boy, the present average age of all the five is 15 years. The present age of the new boy is

(1) 14 years 

(2) 6 years

(3) 15 years 

(4) 19 years

2.The cost of a piece of diamond varies with the square of its weight. A diamond of Rs. 5,184 value is cut into 3 pieces whose weights are in the ratio l : 2 : 3. Find the loss involved in the cutting.

(1) Rs. 3,068 

(2) Rs. 3,088

(3) Rs. 3.175 

(4) Rs. 3,168

3.A discount of 30% on the marked price of a toy reduces its selling price by Rs. 30. What is the new selling price (in Rs.)?

(1) 70  

(2) 21 

(3) 130  

(4) 100 

4.Pipe A alone can fill a tank in 8 hours. Pipe B alone can fill it in 6 hours. If both the pipes are opened and after 2 hours pipe A is closed, then the other pipe will fill the tank in 

(1) 6 hours   

(2) 3.5 hours

(3) 4 hours 

(4) 2 .5 hours

5.The population of a town is 15000. If the number of males increases by 8% and that of females by 10%, then the population would increase to 16300. Find the number of females in the town. 

(1) 4000  

(2) 6000

(3) 3000  

(4) 5000

6.If Rs. 5,000 becomes Rs. 5,700 in a year's time, what will Rs. 7,000 become at the end of 5 years at the same rate of simple interest?

(1) Rs.10, 500 

(2) Rs. l1, 900 

(3) Rs. 12, 700 

(4) Rs. 7,700

7.A thief is noticed by a policeman from a distance of 200 m. The thief starts running and the policeman chases him. The thief and the policeman run at the rate of 10 km and 11 km per hour respectively. The distance (in metres) between them after 6 minutes is

(1) 190 

(2) 200 

(3) 100 

(4) 150

8.‘A’ sells an article to ‘B’ at a profit of 20% and ‘B’ sells it to ‘C’ at a profit of 25%. If ‘C’ pays Rs.1200,the cost price of the article originally (in Rs.) is 

(1) 700  

(2) 600 

(3) 1,000 

(4) 800 

9.The least number which when divided by 35,45, 55 leaves the remainder 18,28,38 respectively is

(1) 3448 

(2)3482  

(3) 2468

(4) 3265

10.A farmer divides his herd of n cows among his four sons, so that the first son gets one-half the herd, the second one- fourth, the third son 1/5 and the fourth son 7 cows. Then the value of n is

(1) 240  

(2) 100 

(3) 180  

(4) 140

ANSWERS AND SOLUTION :
1.(4) Sum of the present ages of four boys
= 9 * 4 + 20 = 56 years
Sum of the present ages of five boys
= 15 * 5 = 75 years
so Present age of new boy
= 75 – 56 = 19 years

2.(4) If the weight of  a piece of diamond be 6 x units, then Original price α(6x)^2 = 36kx^2
so 36.kx^2 = 5184 ………(i)
Again,
New price = k(x^2 + 4x^2 + 9x^2)
= 14kx^2
= (14 * 5184)/36 = Rs. 2016
so Loss = 5184 – 2016
= Rs. 3168

3.(1) 30% = Rs. 30
so 100% = Rs. 100
New S.P. = 100 -30 = Rs. 70

4.(4) Part of the tank filled by both pipes in two hours
= 2 (1/8 + 1/6) = 2(3 + 4)/24 = 7/12
Remaining part = 1 – 7/12 = 5/12
Time taken by B in filling the remaining part
= 5/12 * 6 = 5/2 = 2 1/2 hours

5.(4) If the number of females be x, then number of males = 15000 – x
so x * 10/100 + (15000 –x) * 8/100
= 16300 – 15000
= 10x + 120000 – 8x
= 1300 * 100
=> 2x = 130000 – 120000 = 10000
=>x  = 5000
 
6.(2) Interest = 5700 – 5000
= Rs. 700
so Rate = (700 * 100)/(5000 * 1) = 14%
Case II,
Interest = Principal * Time * Rate/100
= (7000 * 5 * 14)/100 = Rs. 4900
Amount = 7000 + 4900
= Rs. 11900
 
7.(3) Relative speed = 11 – 10 = 1 kmph
Distance covered in 6 minutes
= 1000/60 * 6 metre = 100 metre
so Remaining distance =200-100=100
 
8.(4) Effective profit percent
= (20 + 25 + (20 * 25)/100) = 50%
so Original  cost price = 100/150 * 1200 = Rs.800

9.(1)
10.(4) According to the question.
n/2 + n/4 + n/5 + 7 = n
=> (10n + 5n + 4n)/20  + 7 = n
=> 19n/20 + 7 = n
=> n – 19n/20 = 7
=> n/20 = 7
=> n = 20 * 7 = 140