Quantitative Aptitude

1. The average age of 40 boys in a class is 15. The average age of a group of 18 boys in the class is 16 and the average age of another12 boys in the class is 14. What is the average age of the remaining boys in the class?
(1) 15•25 years  
(2) 14.4 years 
(3) 14•75 years  
(4) None of these

2. Ruby invested an amount of Rs. 5,800 for 2 years. At what rate of compound interest will she get an amount of Rs. 6394•5 at the end of two years ?
(1) 5 p.c.p.a.   
(2) 4 p.c.p.a.
(3) 6 p.c.p.a.   
(4) 8 p.c.p.a.

3. A boat covers a distance of 30 km downstream in 2 hours while it takes 6 hours to cover the same distance upstream. How much time the boat will take to cover 90 km in still water?
(1) 6 hrs   
(2) 9 hrs
(3) 15 hrs   
(4) None of these

4. A lent Rs 5000 to B for 2 years and Rs 3000 to C for 4 years on simple interest at the same rate of interest and received Rs 2200 in all from both of them as interest. The rate of interest is
(1) 5%   
(2) 7%
(3) 8%   
(4) None of these

5. Train A and B travel to a place at a speed of 35 and 55 km/h respectively. If car B takes 7/2  hours  less time than A for the journey, the distance of the place is_
(1) 300.25 km  
(2) 400 km
(3) 350.565 km  
(4) 336.875 km 


6. Two numbers are such that if the first is subtracted from six times the second, their difference becomes 71, and if the second be added to 7 times the first , their sum becomes 62. The two numbers are
(1) 19, 7   
(2) 13, 7
(3) 7, 13   
(4)17, 3


7. How much will be the compound interest to be paid on a principal amount of Rs 85,000/- after 3 years at the rate of 6 p.c.p.a?
(1) Rs 16623.36/-  
(2) Rs 16236.36/-
(3) Rs 16326.36/-  
(4) Rs 16632.36/-


8. Yesterday Mansi typed an essay of 5000 words at the speed of 60 words per minute. Today she typed the same essay faster and her speed was 15% more than yesterday. What is the approximate difference in the time she took to type yesterday and the time she took to type today?
(1) 20 minutes  
(2) 30 minutes
(3) 10 minutes  
(4) 40 minutes


9. To Finish a work, B will take three times as long as A and C together and C will take twice as long as A and B together. If the three persons A, B and C together can finish the work in 20 days , then how long will A take to finish the work alone?
(1) 30 days   
(2) 45 days
(3) 48 days    
(4) 60 days


10. A square park is surrounded from outside by a path of 5 meters width. If the area of the path is 1700sq meters, then what is the area of the park?
(1) 3600sq m  
(2) 4900sq m
(3) 5625sq m  
(4) 6400sq m


11. In how many different ways can the letters of word ‘PREVIOUS’ be arranged in such a way that the vowels always come together?
(1) 50400   
(2) 4840
(3) 3260   
(4) 2880

12. A person drove a certain distance by car the speed of 35 km/h and returned on cycle at the speed of 10 km/h, If the whole journey took 18 hours. Then what distance did he drive on car?
(1) 80 km   
(2) 120 km
(3) 140 km   
(4) 150 km

13. A builder decided to build a house in 50 days. He employed 150 men at the beginning and another 80 men after 20 days and completed the work in the stipulated time. If he had not employed the additional men, how many days behind schedule would it have been finished?
(1) 10 days   
(2) 12 days
(3) 15 days   
(4) 16 days

14. A dealer bought an item at 10% discount on its original price. He sold it at 35% more than the original price. What percentage profit did he get?
(1) 25%   
(2) 45%
(3) 22.5%   
(4) 50%

15. Price register an increase of 10% on food grains and 15% on other items of expenditure. If the ratio of expenditure of an employee on food grains and other items be 2:5, by how much should his salary be increased in order that he may maintain the same level of consumption as before? Assume that there is no saving our of his monthly salary of Rs 2590.
(1) 13.57%   
(2) 12%
(3) 13%   
(4) 18.42%

ANSWERS
1. (2)
Total students are 40 × 15 = 600
So, 18 x 16 + (12 + 14) = 456
Left student is 10 and their average is =600-456= 144÷ 10=14.4

2. (1)
The interest in 2 years is 594.5 which is 10.25% of 5800. Hence the rate of interest is 5% p.a.

3. (2)
Upstream speed = 5 km/hr
Downstream speed = 15 km/hr
Speed of boat in still water = (5 + 15)/2 = 10 km/hr
Required time = 90/10 = 9 hrs

4. (5)
Let the rate of interest is=x
(X * 5000 * 2)/100 + (3000 * 4 * x)/100 = 2200
x = 10%

5. (4)
Let Car A takes t hrs to reach  the place
Distance is same,
35 t = 55(t – 7/2)
T = 77/8
Distance = 35 * 77/8 = 336.87 km

6. (3)
Let the number  be X and Y
Then 6y – x = 71 and 7x + y = 62
 Solving the equation
X = 7,  y = 13

7. (2) C.I. = 85000 × (19.1016/100)
= Rs 16236.36 Approx.

8. (3) Difference of time = 5000/60 − 5000/(60 * 1.15)
= 5000/60 − 5000/69
= 83.33 – 72.46
= 10 min (Approx.)

9. (3)
3*B’s daily work= (A+C)’s daily work
4*B’s daily work = (A+B+C)’s daily work = 1/20 
B’s daily work = 1/80 
2*C’s daily work = (A+B)’s daily work
3*C’s daily work = (A+B+C)’s daily work = 1/20
C’s daily work= 1/60
A’s daily work= 1/20 - (1/80 + 1/60) = 1/48
A can finish the work in 48 days.


10. (4)
Let the side of park be=’x’
Area of path= 2{(x + 10)5 + 5x}

   
1700=2(10x+50)
x = (850 - 50)/10 = 80m 
Area =(80)^2=6400 sq.m

11. (4)
Total letters are ‘8’ and No of vowels = 4
So total no of ways=5! * 4! = 2880

12. (3) Let the distance be x km
Time taken by car = x/35 and time taken on cycle = x/10
x/10 + x/35 = 18
 
13. (4) ,Let 150 men complete the work in x days , work done by 150 men in 20 days +work done by 230 men in 30 days=1
20/x + (230 * 30)/150x = 1
x = 66 days 
So it is 66-50 = 16 days behind the schedule

14. (4)
Let the original price to be Rs 100.
So he bought it at 10% discount ie Rs 90 and sells it at 35% more than the original rate ie Rs 135.
Actual profit is 135-90=Rs 45
So % profit = 45/90 * 100 = 50%

15.(1)
By the method of allegation:

Or, (15  - x)/(x - 10) = 2/5
Or, 75- 5x=2x-20
Or, 7x=95
Or, x=13.57%