## 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 %

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**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