**Percentage questions for competitive entrance exams with Solutions**

Percentage questions for competitive entrance exams with Solutions are created here for helping the candidates who are pursuing competitive entrance exams. Percentage questions for competitive entrance exams with Solutions will help you in clearing all the questions which are generally asked in the quantitative aptitude test of almost every government jobs entrance exam.

**Percentage questions for competitive entrance exams with Solutions**

The percentage is represented by % which means out of hundred, mathematically we write it 1/100

As an example x % =x/100

Conversion of number into a percentage, we can simply multiply a number by 100

As an example 6 is converted into a percentage by multiplying it by 100 i.e 600%

**The formula of percentage which is used for calculating the questions on percentage is**

The percentage of x things out of y things = x thing×100/y things

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**Percentage questions for competitive entrance exams with Solutions**

**Q1.A batsman scored 110 runs which included 3 boundaries and 8 sixes. What percent of his total score did he make by running between the wickets?**

**a.44 and 4/11 b. 45 and 9/11 c.43 and 7/11 d. 45 and 5/11**

Ans. d. 45 and 5/11

Total score of the batsman is 110

Runs from 3 boundaries are =3×4 =12

Runs from 8 sixes are =8×6 =48

Runs from boundaries and sixes are =48 +12 =60

Runs made by him running between the wickets =Total score – Runs from boundaries and sixes=110 – 60=50

Percent of runs made by him running between the wickets=[ Runs made by him running between the wickets/Total score]×100= (50/110)×100 =45 and 5/11

**Q2.Two students appeared at an examination. One of them secured 9 marks more than the other and his marks was 56% of the sum of their marks. The marks obtained by them are:**

**a. 24,33 b.42,51 c.28,37 d.33,42**

Ans.Let the marks of one student is x then marks of other student is x +9

The sum of the marks obtained by them is = x +x +9 =2x +9

It is given that

Marks of one student = 56% of the sum of their marks

x +9= 56% of (2x +9)

x +9= 56/100(2x +9)

100x +900=112x + 504

12x = 900 -504 =396

x =396/12 =33

Marks obtained by them are 33 and 33 +9=42

**Q3.A fruit seller had some apples. He sells 40% apples and still has 420 apples. Originally, he had**

**a.500 b.520 c.600 d.700**

Ans.Let the fruit seller had x apples

The apples sold by him = 40% of the x =40x/100 =2x/5

According to question

x -40% of the x =420

x -40x/100 =420

x -2x/5 = 420

3x/5 =420

x =(420×5)/3 =600

**Q4.What percentage of numbers from 1 to 70 have 1 or 9 in the unit’s digit?**

**a.20 b.10 c.40 d.30**

Ans. The numbers from 1 to 70 have 1 or 9 in the unit’s digit are

1,9,11,19,21,29,31,39,41,49,51,59,61,69(i.e 14)

Total numbers from 1 to 70 are =70

Percentage of numbers from 1 to 70 have 1 or 9 in the unit’s digit =( numbers from 1 to 70 have 1 or 9 in the unit’s digit)×100/Total numbers from 1 to 70

= [14/70]×100 = 20

**Q5.If 20% of a = b, then b% of 20 is the same as:**

**a.5% of a b.4% of a c.10% of a d.15% of a**

Ans. It is given that

20% of *a* = *b*

20a/100 =b

a/5 =b

b % of 20 = (a/5) % 20 =[20a/100].1/5= 4a/100 =4% of a

**Q6.In a certain school, 20% of students are below 8 years of age. The number of students above 8 years of age is 2/3 of the number of students of 8 years of age which is 48. What is the total number of students in the school?**

**a.90 b.80 c.200 d.100**

Ans. Let the total number of students in the school are =x

The no.of students below 8 years =20% of x =20x/100 =x/5

The no. of students of 8 years = 48

The no.of students above 8 years =2/3 of 48 =32

Total students = 48 +32 +x/5

x = 48 +32 +x/5

x – x/5 =80

4x/5 =80

x =(80×5)/4 =100

**Q7.Two numbers A and B are such that the sum of 5% of A and 4% of B is two-thirds of the sum of 6% of A and 8% of B. Find the ratio of A : B.**

**a.2 : 3 b.3 : 4 c.5: 3 d.4 :3**

Ans. According to question

Sum of 5% of A and 4% of B = 2/3[sum of 6% of A and 8% of B]

5A /100+4B/100 = 2/3[6A/100 +8B/100]

(5A +4B)/100 =2/3(6A +8B)/100

5A +4B = 2/3(6A +8B)

15A +12B =12A + 16B

3A = 4B

A/B =4/3

A : B = 4 : 3

**Q8.A student multiplied a number by 3/5 instead of 5/3. What is the percentage error in the calculation?**

**a.22% b.30% c.25% d.64%**

Ans. Percentage error = The difference in the outcomes×100/Actual outcome

The difference in the outcomes =5/3 – 3/5 =16/15

Actual outcome = 5/3

∴Percentage error =[16/15 ÷ 5/3]×100 =[16/15 × 3/5]×100 =[48/75]×100 =64 %

**Q9.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.2200 b.3000 c.2500 d.2700**

Ans. Total votes are 7500

Invalid votes are 20 %,therefore valid votes are 80%

Valid votes are =80% of 7500 =(80/100)×7500=6000

One candidate got the votes =55% of the total valid votes then other would get 45 % of the total valid votes

Valid votes that the other candidate got =45 % of 6000 =(45/100)×6000= 2700

**Q10.Three candidates contested an election and received 1136, 7636 and 11628 votes respectively. What percentage of the total votes did the winning candidate get?**

**a.67% b.37% c.57% d.64%**

Ans. The winning candidate received 11628 votes

Three candidates got the total number of votes =1136 + 7636 + 11628=20400

Percentage of votes of winning candidates =(the number of votes received by winning candidates×100)/(Votes of all three candidates)

= 11628×100/20400= 57 %

**Q11.Two tailors X and Y are paid a total of Rs. 550 per week by their employer. If X is paid 120 percent of the sum paid to Y, how much is Y paid per week?**

**a.Rs 200 b.Rs 250 c.Rs 300 d.Rs 350**

Ans. Let the Y is paid y rupees per week

Money paid to X =120% of y =120y/100 =6y/5

The money paid to the tailors X and Y is Rs. 550 per week

Money paid to X + Money paid to Y = Total money paid to the tailors X and Y

6y/5 + y = 550

(6y +5y)/5 = 550

11y/5 =550

y = (550 ×5)/11 =50×5 =250

∴ Y is paid Rs 250 per week

**Q12.Gauri went to the stationers and bought things worth Rs. 25, out of which 30 paise went on sales tax on taxable purchases. If the tax rate was 6%, then what was the cost of the tax-free items?**

**a.Rs 20.70 b.Rs 18.70 c.Rs 19.70 d.Rs 21.70**

Ans.Let the amount of taxable purchase be Rs x

Tax rate is = 6%

Tax =6x/100 =30 painse =Rs 0.30

x = (0.30 ×100)/6 = Rs 5

The money paid on taxable purchasble = 5 +0.30 =Rs 5.30

Hence cost of the tax-free items =Rs (25 -5.30) = Rs 19.70

**Q13.Rajeev buys good worth Rs. 6650. He gets a rebate of 6% on it. After getting the rebate, he pays sales tax @ 10%. Find the amount he will have to pay for the goods.**

**a.Rs 7200.10 b.Rs 6876.10 c.Rs 5876.10 d.Rs 6587.10**

Ans.The worth of goods = Rs 6650

Rebate on goods = 6%

Rebate on goods of the worth =6 % of 6650 =(6 ×6650)/100 =Rs 399

The cost of the goods after the rebate = 6650 – 399 = Rs 6251

Sales tax = 10 % of 6251 =Rs 625.1

The amount he will have to pay for the goods =Rs 6251 +Rs 625.1 =Rs 6876.10

**Q14.The population of a town increased from 1,75,000 to 2,62,500 in a decade. The average percent increase of population per year is:**

**a.6% b.Rs 7% c.5% d.10%**

Ans. Increased population in a decade = 2,62,500 -1,75,000=87500

% of incresed population in a decade =Increased population in a decade×100/initial population=87500×100/1,75,000=50%

Average population increase in per year =(50/10) % =5 %

**Q15.A man spends 35% of his income on food, 25% on children’s education and 80% of the remaining on house rent. What percent of his income he is left with ?**

**a.8% b.Rs 7% c.5% d.10%**

Ans.Let his total income =Rs 100

His spend on food = Rs 35

Spend on children’s education = Rs 25

His remaining income =Rs[ 100-(35 +25) =Rs (100 -60)=Rs40

Spend on house rent = 80 % of 40 =Rs 32

The remaining income after paying house rent =Rs(40 -32) =Rs 8

**The percent of his income he is left with 8 %**

**Q17.Fresh fruit contains 68% water and dry fruit contains 20% water. How much dry fruit can be obtained from 100 kg of fresh fruits ?**

**a.30 kg b.40 kg c.35 kg d.50 kg**

Ans. Fresh fruits are 100 kg

We have to obtain the amount of dry fruits from 100 kg of fresh fruits

Fresh fruit contains 68 % water and 32 % dried portion of fruit

Dried fruits contain 20% water and 80 % of dry fruits

∴ 32 % dried portion of 100 kg fresh fruit = 80 % dried portion of dry fruit

(32×100)/100 =(80/100)dry fruits

dry fruits = 3200/80 = 40 kg

**Q18.If 75% of a number is added to 75, then the result is the number itself. The number is**

**a.200 b.300 c.400 d.250 kg**

Ans. Let the number is =x

75 + 75x/100 = x

75 +3x/4 = x

x -3x/4 = 75

x/4 =75

x = 75×4 =300

**Q19.A’s salary is 40% of B’s salary which is 25% of C’s salary. What percentage of C’s salary is A’s salary ?**

**a.5% b.10% c.20% d.15%**

Ans. Let C ‘s salary is Rs100

Then B’s salary is 25 % of C ‘s salary

B’s salary = Rs 25

A’s salary = 40% of 25 =(40/100)×25 =Rs 10

% of A’s salary of C’s salary =(10×100/100)=10%

**Q20.A salesman gets a commission on total sales at 9%. If the sale is exceeded Rs.10,000 he gets an additional commission as a bonus of 3% on the excess of sales over Rs.10,000. If he gets a total commission of Rs.1380, then the bonus he received is:**

Ans. Let the total sale is =x and his total commission is Rs.1380

A salesman gets a commission on total sales at 9% and an additional commission as a bonus of 3% on the excess of sales over Rs.10,000

9 % of x+3% of (x -10000) = 1380

9x/100 +3x/100- 300 = 1380

12x/100 =1380 +300 = 1680

x = (1680×100)/12 = 14000

His excess sale is 16000 – 14000 =Rs 4000

His bonus is = 3% of 4000 =Rs 120

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