Question 1

The sum of 15% of a positive number and 20% of the same number is 126. What is one-third of that number

Accepted Answer

Let the positive number be N. According to the question N x (15+ 20)% = 126 ⇒ N x 35 = 126 x 100 ∴ N = 12600/35 = 360 So, one-third of the number = 360/3 = 120

Question 2

In a test, A scored 10% more than B and B scored 5% more than C. If C scored 300 marks out of 400, then A's marks are

Accepted Answer

B's marks = C's marks + 5% of 400 = 300 + 20 = 320 Now , A's marks = B's marks + 10% of 400 = 320 + 40 = 360

Question 3

Mathew scored 42 marks in Biology, 51 marks in Chemistry, 58 marks in Mathematics, 35 marks in Physics and 48 marks English. The maximum marks, a student can score in each subject, are 60. How much overall percentage did Mathew get in this exam?

Accepted Answer

Total marks scored by Mathew in all subjests = 42 + 51 + 58 + 35 + 48 = 234 ∵ Maximum marks is 60 in any subject. ∴ Maximum marks = 60 x 5 = 300 ∴ Percentage of Mathew's marks = [(Marks obtained / Maximum marks)] x 100 = (234 / 300) x 100 = 234/3 = 78%

Question 4

A student was asked to measure the length and breadth of a rectangle. By mistake, he measured the length 20% less and the breath 10% more. if its original area is 200 sq cm, then find the area after this measurement?

Accepted Answer

Net effect on area = -20 + 10 + [(-20 )(10)/100] % = (-10 - 2) % = -12% Now, after this mistake new area = (100 - 12)% of 200 = (88/100) x 200 = 176 sq cm

Question 5

A box has 100 blue balls, 50 red ballss and 50 black balls. 25% of blue balls and 50% of red balls are taken away. Then, percentage of black balls at present is?

Accepted Answer

After removing 25% of blue balls, Total blue balls left = 75% of 100 = (75/100) x 100 = 75 After removing 50% of red balls, total red balls left = 50% 0f 50 = (50 x 50) / 100 = 25 ∴ Required percentage = [50/(75 + 25 + 50)] x 100 = (50/150) x 100 = 331/3 %

Question 6

The price of two article are as 3 : 4. If the price of the first article is increased by 10% and that if the second by ₹ 4 one original ratio remains the same. The original price of the second article is

Accepted Answer

Let cost prices of two article be 3N and 4N respectively then (110% of 3N) / (4N + 4) = 3/4 ⇒ 1.1N / (N + 1) = 1 ⇒ 1.1N = N + 1 ⇒ 0.1 N = 1 ⇒ N = 10 Thus, cost price of the second article is 4 x 10 = ₹ 40

Question 7

from 2008 to 2009, the sales of a book decreased by 80%. If the sales in 2010 was the same as in 2008, by what per cent did it increase from 2009 to 2010?

Accepted Answer

Let sale in 2008 = 100 Sale in 2009 = 20 Sale in 2010 = 100 ∴ Required increases = [(100 - 20)/20] x100 = (80/20) x 100 = 400%

Question 8

In a particular constituency, 75% of voters cast their votes, out of which 2% were rejected. The winning candidate received 75% of the valid votes and bagged a total of 9261 votes. The total number of voters in the constituency is

Accepted Answer

Let the total number of votes = N According to the question, 75% of 98% of 75% of N = 9261 [∵ 2% votes were rejected] ⇒ (N x 75 x 98 x 75) / (100 x 100 x 100) = 9261 ∴ N = (9261 x 100 x 100 x 100) / (75 x 75 x 98) = 16800

Question 9

Last year, there were 610 boys in a school. The number decreased by 20% this year. How many girl are there in the school, if the number of boys in the school this year?

Accepted Answer

Last year number of boys in school = 610 ∴ Number of boys in school this year = 610 - (610 x 20)/100 = 610 - 122 = 488 ∴ Number of girls in school this year = Number of boys in school this year x 175% = (488 x 175)/100 = (488 x 7)/4 = 122 x 7 = 854 Hence, number of girls in school this year in 854.

Question 10

Aryan got 350 marks and Vidya scored 76% marks in the same test. If Vidaya scored 296 marks more than Aryan, then what were the maximum marks of the test?

Accepted Answer

Let maximum marks of the exam is N. According to the question, Marks obtained by Vidaya = Marks obtained by Aryan + 296 ⇒ N x (76/100) = 350 + 296 ⇒ N x (76/100) = 646 ⇒ N = (646 x 100)/7 ⇒ N = 8.5 x 100 = 850 ∴ N = 850

Question 11

What should come in place of the question marks(?), so that it satisfies equality of the given equation? 32% of 750 =?

Accepted Answer

32% of 750 = 750 x (32/100) = 240 From option (a), 23% of 600 = 600 x 23/100 = 138 From option (b), 46 % of 207 = 207 x 46/100 = 95.22 From option (c), 98% of 250 = 250 x 98/100 = 245 From option (d), 75% of 320 = 320 x 75/100 = 240 Hence, from option (d), satisfies equality of the equation.

Question 12

In a class X of 30 students, 24 passed in first class; in another class Y of 35 students, 28 passed in first class. In which class was the percentage of students first class more?

Accepted Answer

For class X, let the students passed in first class = a% Then, by condition given in question a% of 30 = 24 ⇒ (a x 30) /100 = 24 ∴ a = 80% Now, for class Y let the student passed in first class = b% Then, according to the question, b% of 35 = 28 ⇒ (b x 35)/100 = 28 ∴ b = (28 x 100)/35 = 80% Hence, both classes have equal percentage of student getting first class.

Question 13

Veena spends 25% of her monthly income on household expenses. Her annual income is ₹ 4.32 lakh. What is the total amount that Veena spends on household expenses in 8 months together?

Accepted Answer

Annual household expenses = ₹ (25% of 4.32 x 105) = ₹ (25/100) x 4.32 x 105 = ₹ ( 25 x 4.32 x 103) ∴ Household expenses for 8 months = ₹ [(25 x 4.32)/(12 x 8)] x 103) = ₹ 72000

Question 14

The salary of an employee of a company increase every month by 4%. If his salary in August was ₹ 6300, then what would be his approximate salary in month of October of the same year?

Accepted Answer

Required salary in October = 6300 x (104/100) x (104/100) = 63 x 104 x 1.04 = ₹ 6814.08 ≈ ₹ 6814

Question 15

1 L of water is added to 5 L of alcohol and water solution containing 40% alcohol strength. The strength of alcohol in the new solution will be?

Accepted Answer

Quantity of alcohol in 5 L of solution = (40/100) x 5 = 2 L Quantity of alcohol in 6 L of solution = 2 L ∴ Strength of alcohol in new solution = (2/6) x 100% = 331/3%

Question 16

In an examination, 49% students failed in English, 36% students failed in Hindi, While 15% failed in both. if total number of passed students in 450, then how many students did appear in the examination?

Accepted Answer

According to the formula . Percentage of students passed in both the subjects = [100 - (x + y - z)]% = [100 - (49 + 36 - 15)]% = 30% Let total number of students = N According to the question, (N x 30)/100 = 450 ⇒ N = (450/30) x 100 = 1500 ∴ Total number of students = 1500

Question 17

Bina's monthly income is 90% of Anita's monthly income. The total of both their monthly income is Mr. Sen's monthly income. Mr. Sen's annul income is ₹ 775200. What is Bina's monthly income?

Accepted Answer

Mr. Sen's monthly income = (Bina + Anita)'s monthly income = 775200/12 = ₹ 64600 According to the question. Bina's monthly income = 90% of Anita's monthly income ⇒ Bina/Anita = 90/100 = 9 /10 ⇒ Bina : Anita = 9 : 10 ∴ Bina's Monthly salary = (9/19) x 64600 = ₹ 30600

Question 18

In an examination, it is required to get 296 marks out of aggregate marks to pass. A students gets 222 marks and is declared failed by 10% marks . What are the maximum aggregate marks a students can get?

Accepted Answer

Let the maximum aggregate marks be N According to the question, 10% of N = 296 - 222 ⇒ N/10 = 74 ∴ N = (74 x 10) = 740

Question 19

In an office, 40 % of the staff is female. 40% of the female and 60% of the male voted for me. The percentage of votes I got was

Accepted Answer

Let the total number of staff be 100. ∴ Female staff = 40 Male staff = (100 - 40) = 60 Votes cast by females = (40/100) x 40 = 16 Votes cast by males = (60/100) x 60 = 36 Votes cast by both (males + females) = 16 + 36 = 52 ∴ Percentage votes obtained = 52%

Question 20

A reduction of 20% in the price of wheat enables a person to buy 3.5 kg more wheat for ₹ 770. The original price of rice is?

Accepted Answer

Here, R = 20%, A = 3.5 kg and P = ₹ 770 According to the formula , Actual price of rice = [PR /(100 - R)] A = [(20 x 770) / (100 - 20)] x 3.5 = [(20 x 770) / (80 x 3.5) = ₹ 55

Percentage Questions