Question 1

In an examination, 40% students failed in Hindi, 50% student failed in English. If 21% student failed in both the subject find the percentage of those who passed in Hindi?

Accepted Answer

Clearly, it is given that 40% failed in Hindi, so those who passed in Hindi = (100 - 40)% = 60%

Question 2

A student attempted 24 question and secured full marks in all of them. If he obtained 40% in the test and each question carried equal marks, then what was the total number of questions in the test?

Accepted Answer

40% = 24 questions. ∴ Total question = (100/40) x 24 = 60

Question 3

In a town 25% families own a phone and 15% own a car, 65% families own neithers a phone nor a car. 2000 families own both a phone and a car. Consider the following statement in this regard. (i) 10% families own both a car and a phone. (ii) 35% famil…

Accepted Answer

Suppose N% familes own both a car and a phone, then percentage of the families owing only a phone = 25 - N Percentage of the families owing only a car = 15 - N ∴ (25 - N) +(15 - N) + N + 65 = 100 ⇒ N = 5 Percentage of families who have either a car or a phone = (25 - 5) + (15 - 5) + 5 = 35 So, Statement ll is correct. Now, suppose the total number of families in the town be A. ∴ (5 x A)/100 = 2000 ⇒ A = 40000 So, Statement lll is also correct.

Question 4

In a company, 60% of the employees are men. Of these 40% are drawing more than ₹ 50000 per year. If 36% of the total employees of the company draw more than₹ 50000 per year, then what is the percentage of women who are drawing less than ₹ 50000 per …

Accepted Answer

Let total number of employee be 100. ∴ Number of men = 60% of 100 = 60 and number of women = 40% of 100 = 40 Number of men drawing more than ₹ 50000 = 40% of 60 = 24 men Since, number of total employees drawing more than ₹ 50000 = 36% of 100 = 36 Number of women who more than ₹ 50000 = 36 - 24 = 12 Number of women who draw less than ₹ 50000 = 40 - 12 = 28 Percentage of women who draw less then ₹ 50000 per year = (28 x 100)/40 = 70%

Question 5

720 sweets were distributed equally among children in such a way that number of sweets received by each child is 20% of the total number of children. How many sweets did each receive?

Accepted Answer

Let the total number of children be N. Then, N x (20/100) x N = 720 ⇒ N2/5 = 720 ⇒ N2 = 5 x 720 = 5 x 5 x 144 ∴ N = √5 x 5 x 144 = 60 Number of sweets received by each child = (20/100) x 60 = 12

Question 6

A pot is filled with alcohal. 80% of alcohal is replaced by the same quantity of water. This process is done three times. Find the percentage of alcohal in this mixture of alcohal and water.

Accepted Answer

Let quantity of alcohal = 1000 L Quantity of alcohal after 1st process = 80% of 1000 L = 800 L Quantity of alcohol after 2nd process = 80% of 800 L = 640 L Quantity of alcohol after 3rd process = 80% of 640 L = 512 L ∴ Required percentage = (512/1000) x 100 = 51.2%

Question 7

If the price of petrol is increased by 20% by what percentage should the consumption be decreased by the consumer, if the expenditure on petrol remain unchanged?

Accepted Answer

Here, a = 20% Required percentage loss = [a / (100 + a)] x 100% = [20/(100 + 20)] x 100% = (20/120) x 100% = 162/3%

Question 8

There are 1240 employee in an organization. Out of which, 25% are promoted. How many such employees are there who got promotion?

Accepted Answer

Require number = 1240 x (25/100) = 310

Question 9

The difference between 78% of a number and 59% of the same number is 323. What is 62% of that number

Accepted Answer

Let the number be N. According to the question, (78 - 59)% of N = 323 ⇒ (19 x N)/100 = 323 ∴ N = (323 x 100)/19 = 1700 ∴ 62% of 1700 = (62/100) x 1700 = 1054

Question 10

A water pipe is cut into two pieces. The longer piece is 70% of the length of the pipe. By how much percentage is the longer piece longer than the shorter piece?

Accepted Answer

Increase in percentage of longer pipe compared to shorter pipe = [(70 - 30)/30] x 100% = (40/30) x 100% = 400/3 %

Question 11

The marked price of brand A watches is 15% higher than its original price. Due to increased in demand, the price is further increased by 10%. How much profit will be obtained in selling the watches?

Accepted Answer

Given that, a = 15% and b = 10% According to the formula, Required profit = a + b + (ab/100) % = 15 + 10 + (15 x 10)/100 % = (25 + 1.5)% = 26.5% = 26.5%

Question 12

In an examination, 25% students failed in mathematics 20% students failed in Mathematics, 20% failed in Economics and 5% failed in both. Find the percentage of students who passed in both the subjects.

Accepted Answer

Here, x = 25, y = 20 and z = 5 According to the formula, Required percentage = [100 - (25 + 20 - 5)]% = [100 - (45 - 5)]% = (100 - 40)% = 60%

Question 13

If the numerator of a fraction is increased by 200% and the denominator of the fraction is increased by 150%, the resultant fraction is 9/35 .What is the original fraction.

Accepted Answer

Let the fraction be P/Q. Then, (P + 2P)/ Q + 3/2Q = 9/35 ⇒ (3P/5Q) x 2 = 9/35 ∴ P/Q = (9/35) x (5/6) = 3/14

Question 14

Sahil got 45 marks in Hindi, 47 marks in Science, 49 marks in Mathematics, 45 marks in Social Science and 32 marks in English. The Maximum marks of each subject is 50. How much overall percentage of marks did he get?

Accepted Answer

Total marks obtained = [45 + 47 + 49 + 45 + 32] = 218 Maximum marks = 5 x 50 = 250 ∴ overall percentage = (218/250) x 100% = 87.2%

Question 15

A jogger desires to run a certain course in 1/4 less time than he usually takes. By What per cent must be increase his average running speed to accopplish the goal?

Accepted Answer

Let usual speed and usual time taken by the jogger are D and T, respectively. Let his new speed be D'. Then, DT = (3D'/4)T ⇒ D = 3D'/4 ⇒ D' = 4D/3 Thus, he has to increased his speed by [(4D/3 - D) / D] x 100% . = 331/3 %

Question 16

A students was awarded certain marks in an examination. However, after re-evaluation, his marks were reduced by 40% of the marks that were originally awards to him, so that the new score now became 96. How many marks did the student lose after re-ev…

Accepted Answer

Let a student was awarded in exam = N marks According to the question, After re-evaluation his score ⇒ N - N x (40/100) = 96 ⇒ N - 2N/5 = 96 ⇒ 5N - 2N/5 = 96 ⇒ 3N/5 = 96 ⇒ N = (5 x 96)/3 = 5 x 32 ⇒ N = 160 So, a student was awarded by 160 marks in examination ∴ Reduced marks after re-evaluation = 160 - 96 = 64

Question 17

An alloy of gold and silver weights 50g. It contains 80% gold. How much gold should be added to the alloy, so that percentage of gold is increased to 90?

Accepted Answer

Gold in 50g of alloy = (80 x 50)/100 = 40 g Let W gram gold must be added. Now, according to the question, (40 + W) / (50 + W) = 90/100 ⇒ 100( 40 + W) = 90 (50 + W) ⇒ 10(40 + W) = 9 (50 + W) ⇒ 400 + 10W = 450 + 9W ⇒ W = 450 - 400 ⇒ W = 50g Thus, 50 g of gold must be added to make it 90%

Question 18

In a test, Rajesh got 112 marks which was 32 more than the passing marks. Sonal got 75% marks which was 70 more than the passing marks. What is the minimum passing percentage of the test.?

Accepted Answer

Let maximum marks be N . According to the question, 75N/100 - 70 = 112 - 32 ⇒ 75N/100 = 80 + 70 ⇒ 75N/100 = 150 ∴ N = 200 Passing marks = 112 - 32 = 80 (as Rajesh got 112 marks which is 32 more than the passing marks) ∴ Minimum passing marks percentage = (80/200) x 100% = 40%

Question 19

Ram sells his goods 25% cheaper then Shyam and 25% dearer than Hari. How much percentage is Hari's goods cheaper than Shyam?

Accepted Answer

Let the selling price of goods by shyam be = ₹ 100 ∴ Selling price of goods by Ram = ₹ 75 Now, according to the question. 125% of selling price of goods by Hari = 75 ⇒ Selling price of goods by Hari = (100/125) x 75 = ₹ 60 So, Hari's goods are cheaper than shyam's good by (40/100) x 100% = 40%

Question 20

The ratio of the number of boys and girls in a school is 3 : 2. If 20% of the boys and 25% of the girls are scholarship holders, then the percentage of the students who do not get the scholarship, is?

Accepted Answer

Let number of boys be 300. Number of girls = 200 Boys holding scholarship = (20/100) x 300 = 60 Girls holding scholarship = (25/100) x 200 = 50 Total student holding scholarship = 60 + 50 = 110 ∴ Percentage of students not holding scholarship = [(500 -110) / 500] x 100% = (390/500) x 100 % = 78%

Percentage Questions