## Elitmus Previous Year Questions on Percentages

Find answers at the end of every set.

### SET 1

1. A student took five papers in an examination, where the full marks were the same for each paper. His marks in these papers were in the proportion 6: 7: 8: 9: 10. In all papers together, the candidate obtained 60% of the total marks. Then the number of papers in which he got more than 50% marks is?

(a) 1

(b) 3

(d) 5

2. 4/5th of the voters in Bellary promised to vote for Sonia and the rest promised to vote for Sushma. Of these voters, 10% of the voters who had promised to vote for Sonia, did not vote on the election day, while 20% of the voters who had promised to vote for Sushma did not vote on the election day. What is the total no. of votes polled if Sonia got 216 votes?

(a) 200

(b) 300

(d) 100

3. The length, breadth and height of a room are in the ratio 3: 2: 1. If the breadth and height are halved while the length is doubled, then the total area of the four walls of the room will be decreased by?

(a) 13.64%

(b) 15%

(c) 18.75%

4. I bought 5 pens, 7 pencils and 4 erasers. Rahul bought 6 pens, 8 erasers and 14 pencils for an amount which was half more what I had paid. What percent of the total amount paid by me was paid for the pens?

(a) 37.5%

(c) 50%

(d) None of these

5. The number of votes not cast for the Praja Party increased by 25% in the National General Election over those not cast for it in the previous Assembly Polls and the Praja Party lost by a majority twice as large as that by which it had won the Assembly polls. If a total 2,60,000 people voted each time, how many voted for the Praja Party in the previous Assembly Polls?

(a) 1,10,000

(b) 1,50,000

(d) 1,20,000

6. The hourly wages of a female labour are increased by 12.5%, whereas the weekly working hours are reduced by 8%. Find the percentage change in the weekly wages if she was getting Rs 1200 per week for 50 hours previously.

(b) 4%

(c) 4.5%

(d) None of these

7. The price of a Maruti Car rises by 30% while the sales of the car come down by 20%. What is the percentage change in the total revenue?

(a) -4%

(b) -2%

(d) +2%

8. In a survey of political preferences, 78% of those asked were in favour of at least one of the proposals: I, II and III, 50% of those asked favoured proposal I, 30% favoured proposal II and 20% favoured proposal III. If 5% of those asked favoured all three of the proposals, what percentage of those asked favoured more than one of the three proposals?

(a) 10

(b) 12

(d) 22

9. In a class, 25% of the students were absent for an exam. 30% failed by 20 marks and 10% just passed because of grace marks of 5. Find the average score of the class if the remaining students scored an average of 60 marks and the pass marks are 33 (counting the final score of the students).

(a) 37.26

(c) 37.8

(d) 36.93

10.

The owner of an art shop conducts his business in the following manner. Every once in a while he raises his prices by X%, then a while later he reduces all the new prices by X%. After one such up-down cycle, the price of a painting decreased by Rs 441. After a second up-down cycle, the painting was sold at Rs 1944.81. What were the original prices of the painting (in Rs)?

(a) 2756.25

(b) 2256.25

(c) 2500

(d) 2000

Answers-

1. Let the marks scored in five subjects be 6a, 7a, 8a, 9a and 10a.

Total marks in all the five subjects= 40a

Max marks of the five subjects= 40a/0.6

(40a is 60% of total marks)

Hence, Max marks in each subject = 40a/(0.6 x 5)= 13.33a

Hence Percentage in each subject (%)=

*multiply each value by 100.

6a/13.33a= 45.01%

7a/13.33a= 52.51%

8a/13.33a= 60.01%

9a/13.33a=67.51%

10a/13.33a=75.01%

Number of papers in which he got more than 50% marks is 4.

3. Let the length, breadth and height of the room be 3,2 and 1 unit respectively.

Area of the four walls of the room = 2(l + b) h

=2 (3 + 2) x 1= 10 sq unit

New length, breadth and height of the room will be 6, 1 and 1/2 unit respectively.

Hence, new area of the four walls of the room = 2 (6+1) x 0.5= 7 sq unit.

Percentage decrease (%) = 10-7/10=30

4. Pens=A

Pencil=B

Eraser=C

Let, 5A + 7B + 4C = 100 —-(1)

then,

6A + 14B + 8C = 150 —-(2)

Mutliplying equation (1) and (2)

10A + 14B + 8C = 200

Now after solving equation (1) and (3) We get,

A=12.5

Hence, total amount paid for 5A=12.5 x 5=62.5

Hence, Percentage of the total amount paid by(%)=62.5

k

10.

(a) 1

(b) 3

**(c) 4**(d) 5

2. 4/5th of the voters in Bellary promised to vote for Sonia and the rest promised to vote for Sushma. Of these voters, 10% of the voters who had promised to vote for Sonia, did not vote on the election day, while 20% of the voters who had promised to vote for Sushma did not vote on the election day. What is the total no. of votes polled if Sonia got 216 votes?

(a) 200

(b) 300

**(c) 264**(d) 100

3. The length, breadth and height of a room are in the ratio 3: 2: 1. If the breadth and height are halved while the length is doubled, then the total area of the four walls of the room will be decreased by?

(a) 13.64%

(b) 15%

(c) 18.75%

**(d) 30%**4. I bought 5 pens, 7 pencils and 4 erasers. Rahul bought 6 pens, 8 erasers and 14 pencils for an amount which was half more what I had paid. What percent of the total amount paid by me was paid for the pens?

(a) 37.5%

**(b) 62.5%**(c) 50%

(d) None of these

5. The number of votes not cast for the Praja Party increased by 25% in the National General Election over those not cast for it in the previous Assembly Polls and the Praja Party lost by a majority twice as large as that by which it had won the Assembly polls. If a total 2,60,000 people voted each time, how many voted for the Praja Party in the previous Assembly Polls?

(a) 1,10,000

(b) 1,50,000

**(c) 1,40,000**(d) 1,20,000

6. The hourly wages of a female labour are increased by 12.5%, whereas the weekly working hours are reduced by 8%. Find the percentage change in the weekly wages if she was getting Rs 1200 per week for 50 hours previously.

**(a) +3.5%**(b) 4%

(c) 4.5%

(d) None of these

7. The price of a Maruti Car rises by 30% while the sales of the car come down by 20%. What is the percentage change in the total revenue?

(a) -4%

(b) -2%

**(c) +4%**(d) +2%

8. In a survey of political preferences, 78% of those asked were in favour of at least one of the proposals: I, II and III, 50% of those asked favoured proposal I, 30% favoured proposal II and 20% favoured proposal III. If 5% of those asked favoured all three of the proposals, what percentage of those asked favoured more than one of the three proposals?

(a) 10

(b) 12

**(c) 17**(d) 22

9. In a class, 25% of the students were absent for an exam. 30% failed by 20 marks and 10% just passed because of grace marks of 5. Find the average score of the class if the remaining students scored an average of 60 marks and the pass marks are 33 (counting the final score of the students).

(a) 37.26

**(b) 37.6**(c) 37.8

(d) 36.93

10.

The owner of an art shop conducts his business in the following manner. Every once in a while he raises his prices by X%, then a while later he reduces all the new prices by X%. After one such up-down cycle, the price of a painting decreased by Rs 441. After a second up-down cycle, the painting was sold at Rs 1944.81. What were the original prices of the painting (in Rs)?

(a) 2756.25

(b) 2256.25

(c) 2500

(d) 2000

Answers-

1. Let the marks scored in five subjects be 6a, 7a, 8a, 9a and 10a.

Total marks in all the five subjects= 40a

Max marks of the five subjects= 40a/0.6

(40a is 60% of total marks)

Hence, Max marks in each subject = 40a/(0.6 x 5)= 13.33a

Hence Percentage in each subject (%)=

*multiply each value by 100.

6a/13.33a= 45.01%

7a/13.33a= 52.51%

8a/13.33a= 60.01%

9a/13.33a=67.51%

10a/13.33a=75.01%

Number of papers in which he got more than 50% marks is 4.

3. Let the length, breadth and height of the room be 3,2 and 1 unit respectively.

Area of the four walls of the room = 2(l + b) h

=2 (3 + 2) x 1= 10 sq unit

New length, breadth and height of the room will be 6, 1 and 1/2 unit respectively.

Hence, new area of the four walls of the room = 2 (6+1) x 0.5= 7 sq unit.

Percentage decrease (%) = 10-7/10=30

4. Pens=A

Pencil=B

Eraser=C

Let, 5A + 7B + 4C = 100 —-(1)

then,

6A + 14B + 8C = 150 —-(2)

Mutliplying equation (1) and (2)

10A + 14B + 8C = 200

Now after solving equation (1) and (3) We get,

A=12.5

Hence, total amount paid for 5A=12.5 x 5=62.5

Hence, Percentage of the total amount paid by(%)=62.5

k

10.

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