Quant Quiz

Question.1. Shobhit invests Rs. 12000 as fixed deposit at a bank at the rate of 10% per annum simple interest. But due to some pressing needs, he has to withdraw the entire money after 3 yr, for which the bank allowed him a lower rate of interest. If he gets Rs. 3320 less than, what he would have got at the end of 5 yr, the rate of interest allowed by bank is 
(a)12(15/19)%
(b)10(13/17)%
(c)9(9/11)%
(d)8(8/11)%
(e)None of the above

Question.2. Two partners invested Rs. 1250 and Rs.850 respectively in a business. Both the partners distribute 60% of profit equally and distribute the rest 40% as the interest of their capitals .If one partner received Rs. 30 than other.Find the total Profit .
1)Rs. 400
2)Rs. 375.84
3)Rs. 393.75
4)Rs. 380.25 
5)none of these

Question.3. If the circumference of one circle is 5/2 times that of other , how many times the area of smaller circle is the bigger one ?
1)4/25
2)25/24
3)25/4
4)24/25
5)None of these

Question.4. A container contains 50 litres of milk.From this container 5 litres of milk was taken out and replaced by water. This process was repeated further two times. How much milk is now contained by the container?
1) 46.45 liters
2) 27.25 liters
3) 26.14 liters
4) 36.45 liters 
5) None of these

Question.5. The percentage profit earned by selling an article for Rs. 1920 is equal to the percentage loss incurred by selling the same article for Rs. 1280. At what price should the article be sold to make 25% profit?
1) Rs.2500
2) Rs.2000
3) Rs.2200
4) Rs.2800
5) None of these

Question.6. Two pipes can fill a tank in 10 and 14 minutes respectively and a waste pipe can empty 4 gallons per minute. If all the pipes working together can fill the tank in 6 minutes, what is the capacity of the tank?
1) 840 gallons
2) 930 gallons
3) 720 gallons
4) 680 gallons
5) None of these

Question.7. two card is drawn from a pack of 52 cards, each of the 52 cards being equally likely to be drawn find the probability that the card drawn is either black or king. 
1) 63/221
2) 62/231 
3) 37/421 
4) 63/208 
5) None of these

Question.8. Three Science classes A, B and C take an chemistry test. The average score in class A is 93. The average score in class B is 86. The average score in class C is 95. The average score of all students in classes A and B together is 89. The average score of all students in classes B and C together is 91. What is the average score for all the three classes?
1) 81.5
2) 91.5
3) 90
4) 80
5) None of these

Question.9. Find the slant height of a cone whose volume is equal to 3080 m^3 and the diameter of whose base is 28 m. (Ans. in approx. value)
1) 28.5 m 
2) 20.5 m 
3) 43.5 m 
4) 6.5 m 
5) 19.5 m

Question.10. The probability that a leap year selected at random will contain either 53 Monday or 53 Tuesday is-
1) 4/7
2) 6/7
3) 3/7
4) 9/17
5) None of these

Solutions:

Answer.1.(e); 
Let the rate of Interest allowed by bank be r%
(12000X5X10)/100)-((12000X3Xr)/100)=3320
r=7(4/9)%

Answer.2.(3)
(A’s 40% profit)/(B’s 40 % profit) = 1250/850 = 25/17
Using componendo & Dividendo 
40% profit of A and B / 30 = 42/8
So total profit = 42/8 *30*(100/40)= Rs. 393.75

Answer.3.(3)
Ratio of circumference = 5/2
So ratio of area = (5/2)^2 = 25/4

Answer.4.(4)
Amount of milk left after 3 operations 
= 50[1-(5/50)]3 = 50 X (9/10)3 = 36.45 liters

Answer.5.(2)
Let C.P. be Rs. x. 
Then,
[(1920-x)/x]*100 = [(x-1280)*x]/100, 
1920 – x = x – 1280 
2x – 3200= 1600 
hence, x= 1600 
therfore, Required S.P.= 125%of1600= Rs 2000.

Answer.6.(1)
Work done by waste pipe in 1 min = (Part filled by total pipes together) -(part filled by first pipe + part filled by second pipe)
= 1/6 – [(1/10) + (1/14)] = 1/6 – (24/140) = -1/210
Therefore, ATQ-
volume of 1/210 part = 4 gallons
Hence, the capacity of tank = volume of whole = 4 x 210 = 840 gallons.

Answer.7.(1)
When one card is drawn from a pack of 52 cards 
The numbers of possible outcomes n(s) = {52[C]2}= 1326 
Since,
there are 26 black cards and two red king in the pack of 52 cards
then, Numbers of possible favorable outcomes = {28[C]2} = 378 
hence,
Required probability = 378/1326= 63/221

Answer.8.(2)
Let in classes A, B and C number of students are a, b and c 
hence-
(93a + 86b)/(a+b) = 89
and 
(86b + 95c)/(b +c) = 91
Solving these equations we get-
93a + 86b = 89 (a + b) or 4a = 3b or a : b = 3 : 4 
Similarly- 
4c = 5b or b : c = 4 : 5 
Hence
a:b:c = 3 :4 : 5 
So the average for all three classes=(93a+ 86b+ 95c)= (93X3+86X4+95X5)/(3+4+5) 
Average= 91.5

Answer.9.(2) 
Volume of the cone = 1/3 * 22/7 * r^2 * h
1/3 * 22/7 * 14 * 14 * h = 3080
h = (3080 * 3 * 7)/(14 * 14 * 22) = 15 m
Slant height = v{(14)^2 + (15)^2}
= 20.5 m

Answer.10.(3) 
In a leap year 366 day or, 52 week and 2 days. these 2 days will be
1. Sunday and Monday
2. Monday and Tuesday
3. Tuesday – Wednesday
4. Wednesday – Thursday
5. Thursday – Friday
6. Friday-Saturday
7. Saturday – Sunday
Required Probability = 3/7