Percentage Tips & Tricks with Q&A

Percentage Tips & Tricks: Not a single exam In India where quant is there; percentage questions are always asked. They are a core part of the quant syllabus in almost every exam. So, it’s important you solve quality questions along with the right guidance.

Percentage tips & tricks 

• Learn about conversion of fraction into percentage 
• Learn about conversion of percentage into fraction 
• Focus on conceptual building as percentage can help you in solving a lot of quant questions apart from this very topic.  

Here is the list of the percentages and their fractional values till 15 

Percentage Questions – Prelims Level

1.) A student got 28% marks and failed by 150 marks, while another student got 72% marks and scored 180 marks above the passing marks. What is the passing percentage of marks?

a.) 55%

b.) 40%

c.) 42%

d.) 48%

e.) 52%

Answer: d)

Solution:

Let total marks = 100x

So, 72x – 28x = 150 + 180 = 330

So, 44x = 330

So, x = 7.5

Total marks = 750

Passing marks = 0.28 × 750 + 150 = 360

Desired percentage = 360/750 × 100 = 48%

Hence, option d.

2.) Three members A, B and C contested the election. 12% of the votes cast are invalid. Out of the valid votes, A secured 25% votes and B secured 40% votes and won by 77 votes with respect to C. Find the total number of votes (invalid + valid) cast.

a.) 2000

b.) 1250

c.) 1750

d.) 1500

e.) 1420

Answer: c)

Solution:

Let the total number of votes (valid + invalid) cast be ‘x’.

So, number of valid votes = 0.88x

Votes secured by A = 0.88x × 0.25 = 0.22x

Votes secured by B = 0.4 × 0.88x = 0.352x

Votes secured by C = 0.35 × 0.88x = 0.308x

So, 0.352x – 0.308x = 77

0.044x = 77

x = 1750

So, total number of votes (invalid + valid) cast = 1750

Hence, option c.

3.) In a semester examination, 160 students appeared out of which 100 are boys and the rest are girls. 80% of the students scored pass percentage and 10 girls failed. Find the percentage of boys who failed out of the total number of boys.

a.) 15%

b.) 18%

c.) 28%

d.) 24%

e.) 22%

Answer: e)

Solution:

Total number of students who appeared in the semester examination = 160

Number of boys who appeared in the semester examination = 100

Number of girls who appeared in the semester examination = (160 – 100) = 60

Number of students who passed the exam = 0.8 × 160 = 128

Number of girls who failed = 10

Number of boys who failed = (160 – 128 – 10) = 22

Required percentage = 22/100 × 100 = 22%

Hence, option e.

4.) Prashant donates 25% of his monthly income in two NGOs ‘A’ and ‘B’ in the ratio 12:15, respectively. If the amount donated to NGO ‘B’ is Rs. 600 more than that to ‘A’, then find the amount left with Prashant after donation.

a.) Rs. 16200

b.) Rs. 12200

c.) Rs. 16800

d.) Rs. 14200

e.) Rs. 15800

Answer: a)

Solution:

Let the amount donated to NGO ‘A’ and ‘B’ be Rs. 12x and Rs. 15x respectively.

According to the question,

15x – 12x = 600

Or, x = Rs. 200

Total amount donated to all the two NGOs = 27x = Rs. 5400

Monthly income of Prashant = 5400/0.25 = Rs. 21600

Amount left with Prashant = 0.75 × 21600 = Rs. 16200

Hence, option a.

5.) In a class, the total number of students is 300. If the number of boys in the class is ‘x’, then the percentage of the number of girls in the class is x%. Find the percentage of the boys in the class.

a.) 25%

b.) 20%

c.) 15%

d.) 30%

e.) 10%

Answer: a

Solution:

Number of boys in the class = x

Number of girls in the class = (300 – x)

According to the question,

300 × x% = 300 – x

3x + x = 300

4x = 300

x = 75

Number of boys in the class = 75

Number of girls in the class = 225

Required percentage = 75/300 × 100 = 25%

Hence, option a.

Mains:

1.) Population of Palampur is ‘x’. 85% of the population of Palampur is registered in voters list. 25% of the registered voters didn’t cast their votes. 10% of the votes cast are invalid. If in the election between two candidates, the winning candidate got 55% of the valid votes and won by 2,754 votes, then find the value of ‘x’.

a.) 45,000

b.) 48,000

c.) 50,000

d.) 42,000

e.) 54,000

Answer: b)

Solution:

Number of registered voters = 0.85x

Number of votes cast = 0.75 × 0.85 = 0.6375x

Number of valid votes = 0.90 × 0.6375x = 0.57375x

So according to question:

(55 – 45)% of 0.57375x = 2754

0.10 × 0.57375x = 2754

0.057375x = 2754

x = 48,000

Hence, option b.

2.) In an examination, Rajat obtained 27% marks and failed by 77 marks. In the same examination, Priya obtained 49% marks and thus was able to score 165 marks above the passing marks. Find the passing percentage of the examination.

a.) 32%

b.) 34%

c.) 38%

d.) 25%

e.) 40%

Answer: b)

Solution:

Let the maximum marks of the examination = x

Marks obtained by Rajat = 0.27x

Marks obtained by Priya = 0.49x

According to question:

0.27x + 77 = 0.49 – 165

0.22x = 242, x = 1100

Passing marks of the examination = 0.27 × 1100 + 77 = 297 + 77 = 374

So, the passing percentage = (374/1100) × 100 = 374/11 = 34%

Hence, option b.

3.) Village P has 20% more population than Village Q. The respective ratio of the males to female in village P is 8:5. The ratio of males to females in village Q is 5:3 respectively. If the number of males in village P is 3840, then find the difference between the number of females in village P and village Q.

a.) 440

b.) 400

c.) 420

d.) 412

e.) 408

Answer: e)

Solution:

Number of males in village P = 3840

Number of females in village P = 3840 × (5/8) = 2400

Total population of village P = 3840 + 2400 = 6240

Total population of village Q = 1.2 × 6240 = 7488

Number of females in village Q = 7488 × (3/8) = 2808

Required difference = 2808 – 2400 = 408

Hence, option e.

Percentage tips & tricks 

4.) In an election between two candidates for the post of member of a committee, (x + 5)% of the voters didn’t cast their votes while 1100 votes cast were declared invalid. The winner candidate got 2(x + 10)% votes of the voter list and won by 800 votes. Find the value of ‘x’, if the runner up candidate got (4/15) votes of the voter list?

a.) 14

b.) 10

c.) 5

d.) 18

e.) 20

Answer: b)

Solution:

Let, the total number of voters on the voter list be ‘Y’.

According to the question,

Y × 2(x + 10)% + Y × 2(x + 10)% – 800 = Y{100 – (x + 5)}% – 1100

Y(2x + 20 + 2x + 20)% – 800 = Y(95 – x)% – 1100

Y(95 – x – 4x – 40)% = 300

Y(55 – 5x)% = 300 ————-(i)

Also,

Y × 2(x + 10)% – 800 = (4/15)Y

Y[(2x + 20)% – (4/15)] = 800 ———(ii)

Using both equations, we get,

300/(55 – 5x)% = 800/[(2x + 20)% – (4/15)]

3[(2x + 20)% – (4/15)] = 8(55 – 5x)%

6x + 60 – (1200/15) = 440 – 40x

46x = 380 + (1200/15)

46x = 380 + 80

x = 460/46 = 10

Hence, option b.

5.) Mr. Gupta distributed 79% of the money he had among Zeta, Pita and Mega. Amounts received by Zeta and Pita are in the ratio of 7:4 respectively and the amounts received by Mega and Zeta are in the ratio of 5:4 respectively. Find the amount left with Mr. Gupta if the difference between the amounts received by Mega and Pita is Rs. 3800.

a.) Rs. 4,200

b.) Rs. 4,400

c.) Rs. 4,000

d.) Rs. 4,800

e.) Rs. 5,200

Answer: a)

Solution:

Let the amounts received by Zeta and Pita are Rs. 7x and Rs. 4x respectively.

Amounts received by Mega = 7x × (5/4) = Rs. 8.75x

According to question,

8.75x – 4x = 3800

4.75x = 3800, x = 800

So, the total amount distributed by Mr. Gupta = 19.75 × 800 = 15,800

So, the total amount left with Mr. Gupta = 15800 × (21/79) = Rs. 4,200

Hence, option a.

Percentage Tips & Tricks

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Percentage Tips & Tricks

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