Test: Percentages - 1 - UGC NET MCQ

Total number of infected person initially = 230000

Number of people died = 10000

Remaining persons = 230000 – 10000 = 220000

Number of person cured = 43% of 220000 = 94600

Number of person still infected = 220000 - 94600 = 125400

∴ Required percentage = 125400/230000 × 100 = 54.5

Let the total marks be 100x.

Passing marks = 25 x + 15 and 55 x - 15

25x + 15 = 55x - 15

30x = 30

x = 1

Hence, passing marks are 25 + 15 = 40.

Given:

170% of a number added to 66,

the result becomes equal twice

Calculation:

Let the number be = x

According to the question

⇒ x × 170/100 + 66 = 2x

⇒ 17x/10 + 66 = 2x

⇒ 2x - 17x/10 = 66

⇒ 3x/10 = 66

⇒ x = 220

∴ The correct answer is 220.

If the price of petrol has increased from Rs. 40 per litre to Rs. 60 per litre

Let the consumption be 100 litres.

When price is Rs. 40 per litres, then, the expenditure = 100 × 40

⇒ Rs. 4,000.

At Rs. 60 per litre, the 60 × consumption = 4000

Consumption = 4,000/60 = 66.67 litres.

∴ Required decreased % = 100 - 66.67 = 33.33%

Two students appeared for an examination. One of them secured 22

marks more than the other and his marks were 55% of the sum of

their marks

Let the students be A and B

Let the marks secured by B = x

Marks secured by A = x + 22

Sum of their marks of A & B = x + x + 22 = 2x + 22

Accoring to question, 

Marks of A =  55% of the sum of marks

⇒  x + 22 = 0.55 × (2x + 22) 

⇒ x + 22 = 1.1x + 12.1

⇒ 0.1x = 9.9

⇒ x = 9.9/0.1 = 99 marks

Marks secured by A = 99 + 22 = 121 marks

Therefore the correct answer is 121.

From the problem, it is given that

65%x = 45%y

⇒ 13x = 9y

⇒ x = (9/13)y    ----(1)

Given the sum of the numbers = 2574

⇒ (x + y) = 2574     ----(2)

Substituting the value of ‘x’ from Equation 1 in Equation 2, we get

(9/13)y + y = 2574

⇒ (9y + 13y) = 2574 × 13

⇒ 22y = (2574 × 13)

⇒ y = (2574 × 13)/22 = 1521

∴ Value of the larger number is 1521

Let total number of votes be 100 units,

10% voters did not cast their vote

⇒ Votes polled = 90 units

The winning candidate got 53% of all the voters in the list and won by 304 votes,

⇒ Winning candidate got = 53 units votes

⇒ Other candidate got = 37 units votes

⇒ Difference in votes = 53 units votes - 37 units votes = 304 - 48 = 256 votes

⇒ 16 units = 256

∴ 100 units votes = 256/16 × 100 = 1600 votes

∴ Total number of voters = 1600.

We know that

Product of price and consumption is equal to the expenditure

Let the original price of article be x units

According to the question,

Price is increased by 24%

New price of article = x + 16(2/3)% of x = 7x/6

Let the original consumption be y

Original expenditure = xy

Expenditure is increased by 12%

New expenditure = xy + (12/100) × xy = 28xy/25

New consumption = (New expenditure)/(New Price)

New consumption = (28xy/25)/(7x/6) = 24y/25

Decrease in consumption = (y) – (24y/25) = y/25

Required percentage = (y/25)/y × 100 = 4%

Given:

Ratio = 5:4

Formula used:-

Required percentage = (x/y) × 100

Calculation:-

Required percentage = (5/4) × 100

Required percentage = 125%

∴ 5:4 is equal to 125%.

Let the initial oranges with the fruit seller be x.

1^st selling = 0.45x + 1

Remaining = x - (0.45x + 1) = 0.55x - 1

2^nd selling = 15 × (0.55x - 1) = 0.11x - 0.2 + 2 = 0.11x + 1.8

Remaining after second selling = 0.55x - 1 - (0.11x + 1.8) = 0.55x - 0.11x - 1 - 1.8 = 0.44x - 2.8

3^rd selling = 90% × (0.44x - 2.8)

Remaining after 3rd selling = 0.1 × (0.44x - 2.8) = 0.044x - 0.28

According to the question-

⇒ 0.044x - 0.28 = 5

⇒ 0.044x = 5.28

⇒ x = 5.280.044 = 120

∴ The number of oranges was 120.