Quantitative Aptitude Questions And Answers With Explanation. (Practice set 5)

Q:1
In an election between two candidates, one got 55% of the total valid votes, 20% of the votes were invalid. If the total number of votes was 7500, the number of valid votes that the other candidate got, was :
A) 2500 B) 2700
C) 2900 D) 3100
Answer: B) 2700
Q:2
A and B invest in a business in the ratio 3: 2. If 5% of the total profit goes to charity and A's share is Rs. 855, the total profit is :
A) 500 B) 1000
C) 1500 D) 2000
Answer: C) 1500
Q:3
A bag contains 50 P, 25 P, and 10 P coins in the ratio 5: 9: 4, amounting to Rs. 206. Find the number of coins of each type respectively.
A) 360, 160, 200 B) 160, 360, 200
C) 200, 360,160 D) 200,160,300
Answer: C) 200, 360,160
Q:4
A problem is given to three students whose chances of solving it are 1/2, 1/3, and 1/4 respectively. What is the probability that the problem will be solved?
A) 1/4 B) 1/2
C) 3/4 D) 7/12
Answer: C) 3/4
Q:5
The two numbers are respectively 20% and 50% more than a third number. The ratio of the two numbers is:
A) 2:5 B) 3:5
C) 4:5 D) 5:4
Answer: C) 4:5
Q:6
If each side of a square is increased by 25%, find the percentage change in its area?
A) 65.25 B) 56.25
C) 65 D) 56
Answer: B) 56.25
Q:7
A student multiplied a number by 3/5 instead of 5/3, What is the percentage error in the calculation?
A) 54 % B) 64 %
C) 74 % D) 84 %
Answer: B) 64 %
Q:8
If 20% of a = b, then b% of 20 is the same as :
A) 4% of a B) 6% of a
C) 8% of a D) 10% of a
Answer: A) 4% of a
Q:9
Tickets numbered 1 to 20 are mixed up and then a ticket is drawn at random. What is the probability that the ticket drawn has a number which is a multiple of 3 or 5?
A) 1/2 B) 3/5
C) 9/20 D) 8/15
Answer: C) 9/20
Q:10
A bag contains 6 white and 4 black balls .2 balls are drawn at random. Find the probability that they are of the same color.
A) 1/2 B) 7/15
C) 8/15 D) 1/9
Answer: B) 7/15
ANSWERS WITH EXPLANATION
Q:1
Answer: B) 2700
Explanation:
Total number of votes = 7500
Given that 20% of Percentage votes were invalid
=> Valid votes = 80%
Total valid votes = 7500*(80/100)
1st candidate got 55% of the total valid votes.
Hence the 2nd candidate should have got 45% of the total valid votes
=> Valid votes that 2nd candidate got = total valid votes x (45/100)
7500*(80/100)*(45/100) = 2700
Q:2
Answer: C) 1500
Explanation:
Let the total profit be Rs. 100.
After paying to charity, A's share = (95*3/5) = Rs. 57.
If A's share is Rs. 57, total profit = Rs. 100.
If A's share is Rs. 855, total profit = (100/57*855) = 1500.
Q:3
Answer: C) 200, 360,160
Explanation:
Let the ratio be x.
Hence no. of coins be 5x ,9x , 4x respectively
Now given total amount = Rs.206
=> (.50)(5x) + (.25)(9x) + (.10)(4x) = 206
we get x = 40
=> No. of 50p coins = 200
=> No. of 25p coins = 360
=> No. of 10p coins = 160
Q:4
Answer: C) 3/4
Explanation:
Let A, B, C be the respective events of solving the problem, and A, B, C be the respective events of not solving the problem. Then A, B, C are independent event
∴ are independent events
Now, P(A) = 1/2 , P(B) = 1/3 and P(C)=1/4
PA=12, PB=23, PC= 34
∴ P( none solves the problem) = P(not A) and (not B) and (not C)
= PA∩B∩C
= PAPBPC ∵ A, B, C are Independent
= 12×23×34
= 14
Hence, P(the problem will be solved) = 1 - P(none solves the problem)
= 1-14= 3/4
Q:5
Answer: C) 4:5
Explanation:
Let the third number be x.
Then, first number = 120% of x =120x/100 = 6x/5
Second number =150% of x = 150x/100 = 3x/2
Ratio of first two numbers = 6x/5 : 3x/2 = 12x : 15x = 4 : 5
Q:6
Answer: B) 56.25
Explanation:
let each side of the square be a , then area = a²
As given that The side is increased by 25%, then
New side = [5a / 4]²
New area = (5a4)25a42
Increased area= 25a²/16 - a²
Increase %=[9a²/16]/a²*100 % = 56.25%
Q:7
Answer: B) 64 %
Explanation:
Let the number be x.
Then, ideally, he should have multiplied by x by 5/3. Hence Correct result is x * (5/3)= 5x/3.
By mistake, he multiplied x by 3/5. Hence the result with error = 3x/5
Then, error = (5x/3 - 3x/5) = 16x/15
Error % = (error/True vaue) * 100 = [(16/15) * x/(5/3) * x] * 100 = 64 %
Q:8
Answer: A) 4% of a
Explanation:
20% of a = b
=> (20/100) * a = b
b% of 20 =(b/100) x 20 = [(20a/100) / 100] x 20= 4a/100 = 4% of a.
Q:9
Answer: C) 9/20
Explanation:
Here, S = {1, 2, 3, 4, ...., 19, 20}.
Let E = event of getting a multiple of 3 or 5 = {3, 6 , 9, 12, 15, 18, 5, 10, 20}.
P(E) = n(E)/n(S) = 9/20.
Q:10
Answer: B) 7/15
Explanation:
Both the balls are drawn are white2. Both the balls are drawn are Black
Required Probability = P( Both the balls are white) + P(Both the balls are Black)
= 6/10 × 5/9 + 4/10×3/9 = 42/90 = 7/15
So, The Probability is 7/15