### PERCENTAGE QUIZ 001

- A number is increased by 20% and then decreased by 20%, the final value of the number is?

(a) does not change

(b) decreases by 2%

(c) increases by 4%

**(d) decreases by 4%**

(e) None of these

*Explanation:*

Here, x = 20 and y = – 20

Therefore, the net % change in value

= ( x + y + xy/100)%

= [20 – 20 + {20 x (- 20)}/100]% or – 4%

Since the sign is negative, there is a decrease in value by 4%.

- If the income of Mohan is 150% higher than Mahesh, then by what percent the income of Mahesh is less than Mohan?

(a) 40%

(b) 50%

**(c) 60%**

(d) 45%

(e) None of these

*Explanation:*

(c); Required percentage = (150/250) x 100% = 60%

- A man’s wages were decreased by 50%. Again, the reduced wages were increased by 50%. He has a loss of?

(a) 35%

(b) 25%

(c) 20%

**(d) 15%**

(e) None of these

*Explanation:*

Here, x = – 50 and y = 50

Therefore, the net % change in value

= ( x + y + xy/100) %

= [- 50 + 50 + ( -50) x (50)/100]% or – 25%

Since the sign is negative, there is loss of 25%

- By selling 45 lemons for Rs 40, a man loses 20 %. How many should he sell for Rs 24 to gain 20 % in the transaction?

(a) 16

**(b) 18**

(c) 20

(d) 22

(e) None of these

*Explanation:*

- In an election between two candidates, 75 % of the voters cast their votes, out of which 2% of the votes were declared invalid. A candidate got 9261 votes which were 75% of the total valid votes. Find the total number of votes.

(a) 13000

(b) 17000

(c) 19000

**(d) 16800**

(e) 12000

*Explanation:*

Let the total number of votes enrolled are x.

Number of votes cast = 75% of x

Valid votes = 98% of 75% of x

Now, as 9261 is the 75% of valid casted votes so,

75% of 98% of 75% of x = 9261

=>(75×98×75×x)/(100×100×100)=9261=>x=16800

- Rahul’s Mathematics test had 75 problems, 10 arithmetic, 30 algebra, 35 geometry problems. Although he answered 70% of arithmetic, 40% of arithmetic and 60% of geometry problems correctly, still he got less than 60% problems right. How many more questions he would have to answer more to get passed

**(a) 5**

(b) 6

(c) 7

(d) 8

(e) 9

*Explanation:*

Number of questions attempted correctly = (70% of 10 + 40% of 30 + 60% of 35)

= 7 + 12 + 21 = 40.

Questions to be answered correctly for 60% = 60% of total questions

= 60 % of 75 = 45.

He would have to answer 45 – 40 = 5

- Teacher took exam for English, average for the entire class was 80 marks. If we say that 10% of the students scored 95 marks and 20% scored 90 marks then calculate average marks of the remaining students of the class.

(a) 20

(b) 30

**(c) 75**

(d) 60

(e) 80

*Explanation:*

Let’s assume that total number of students in class is 100 and required average be x.

Then from the given statement we can calculate :

(10 * 95) + (20 * 90) + (70 * x) = (100 * 80)

=> 70x = 8000 – (950 + 1800) = 5250

=> x = 75.

- 40% of Ram’s marks is equal to 20% of Rahim’s marks which percent is equal to 30% of Robert’s marks. If Robert’s marks is 80, then find the average marks of Ram and Rahim?

**(a) 90**

(b) 100

(c) 120

(d) 130

(e) 140

*Explanation:*

Given, 40% of Ram’s marks = 20% of Rahim’s marks = 30% of Robert’s marks.

Given, marks of Robert = 80

30% of 80 = 30/100 * 8 = 24

Given, 40% of Ram’s marks = 24.

=> Ram’s marks = (24 * 100)/40 = 60

Also, 20% of Rahim’s marks = 24

=> Rahim’s marks = (24 * 100)/20 = 120

Average marks of Ram and Rahim = (60 + 120)/2 = 90.

- Anil spends 40% of his income on rent, 30% of the remaining on medicines and 20% of the remaining on education. If he saves Rs. 840 every month, then find his monthly salary?

(a) 1800

**(b) 2500**

(c) 2700

(d) 2300

(e) 3000

*Explanation:*

Let’s Anil’s salary be Rs. 100.

Money spent on Rent = 40% of 100 = Rs. 40.

Money spent on medical grounds = 30% of (100 – 40) = 3/10 * 60 = Rs. 18.

Money spent on education = 20% of (60 – 18) = 1/5 * 42 = Rs. 8.40

Anil saves 100 – (40 + 18 + 8.40) i.e., Rs. 33.60

for 33.6 —> 100 ; 840 —> ?

Required salary = (840/33.6) * 100 = Rs. 2500

- A vendor fixed Selling Price of a product at 40% above the cost price. He sells half the stock at this price, one-quarter of that stock at a discount of 25% on the original selling price and rest at a discount of 30% on the original selling price. Find the gain percentage all together?

**(a) 20.75%**

(b) 0.1575

(c) 0.1475

(d) 0.1675

(e) none of these

*Explanation:*

Let CP = 100;

marked price=140;

Revenue = [(1/2)*140 + (1/4)*0.75*140 + (1/4)*0.7*140] = 70 + 26.25 + 24.5 = 120.75;

% profit = 20.75/100 = 20.75%

- From the salary of Rahul, 20% is deducted as house rent, 10% of the rest he spends on children’s education and 10% of the balance, he spends on clothes. After this expenditure he is left with Rs 1,377. His salary is?

**(a) Rs 2,125**

(b) Rs 2,040

(c) Rs 2,100

(d) Rs 2,200

(e) None of these

*Explanation:*

Suppose that his salary = Rs 100

House rent = Rs 20, balance = Rs 80

Expenditure on education = Rs (10 x 80)/100 = Rs 8

Balance = Rs 72

Expenditure on clothes Rs (10 x 72)/100 = Rs 7.2

Balance now = Rs 64.8

If balance is Rs 64.8, salary = Rs 100

If balance is Rs 1,377, salary

= Rs (100 x 1377) / 64.8

= Rs 2,125

- In a class, 60% of the students are boys and in an examination, 80% of the girls scored more than 40 marks (Maximum Marks:150). If 60% of the total students scored more than 40 marks in the same exam, what is the fraction of the boys who scored 40 marks or less.

**(a) 8/15**

(b) 2/5

(c) 4/5

(d) 1/5

(e) none of these

*Explanation:*

Assume Total no of students = 100

60% of the students are boys. so Boys=60,Girls=40

No. of girls who scored more than 40 marks = 80% of girls = 80% of 40 = 32.

No. of students who scored more than 40 marks = 60% of Total Students = 60

Therefore No. of boys who scored more than 40 marks = 60-32=28

No. of boys who scored less= Total boys – Boys(scored more) = 60-28=32

Fraction=(scored less)/Total boys = 32/60 =8/15

- A man purchases some oranges at the rate of 25 for rupee 100 and same amount of oranges at the rate of 50 for rupees 100. He mixes them and sell at the rate of 25 for rupees 75. Find the profit/loss percentage.

(a) 4% loss

(b) 4% profit

(c) 5% loss

**(d) No profit no loss**

(e) None of these

*Explanation:*

Let man buys X unit of oranges at the rate of 25 for rupee 100 and X unit of oranges at the rate of 50 for rupee 100.

CP = (100/25)* X + (100/50)*X = 6X

SP = (75/25)*2X = 6X

So, no profit no loss

- A shopkeeper bought 600 oranges and 400 bananas. He found 15% of oranges and 8% of bananas were rotten. Find the percentage of fruits in good condition.

(a) 80%

(b) 70.08%

**(c) 87.8%**

(d) 90%

(e) None of these

*Explanation:*

Total number of fruits shopkeeper bought = 600 + 400 = 1000

Number of rotten oranges = 15% of 600

= 15/100 × 600

= 9000/100

= 90

Number of rotten bananas = 8% of 400

= 8/100 × 400

= 3200/100

= 32

Therefore, total number of rotten fruits = 90 + 32 = 122

Therefore Number of fruits in good condition = 1000 – 122 = 878

Therefore Percentage of fruits in good condition = (878/1000 × 100)%

= (87800/1000)%

= 87.8%

15. A report consists of 20 sheets each of 55 lines and each such line consists of 65 characters. This report is reduced onto sheets each of 65 lines such that each line consists of 70 characters. The percentage reduction in number of sheets is closest to:

**(a) 20%**

(b) 5%

(c) 30%

(d) 35%

(e) None of these

*Explanation:*

No. of Characters in one line = 65

No. of characters in one sheet = No. of lines × No. of characters per line = 55 × 65

Total number of characters = No. of sheets × No. of characters in one sheet = 20 × 55 × 65 = 71500

If the report is retyped –

New sheets have 65 lines, with 70 characters per line

No. of characters in one sheet = 65 × 70

Number of pages required,

Hence, 16 pages will be required if report is retyped.

Hence, reduction of (20 – 16) = 4 pages

% reduction is = (4/20) x 100 = 20%

- Published in PERCENTAGE