Test: Percentages - 2 - SAT MCQ

Juice of 450 ml contains 5% fruit extract, 25% of pulp.

Amount of pulp = 450 × 25/100 = 112.5 ml

Now, let the amount of water added be ‘x’ ml.

Total volume of juice after adding water = 450 + x

New percentage of pulp = 15%

According to the question

⇒ (450 + x) × 15/100 = 112.5

⇒ (450 + x) = 750

∴ x = 300 ml

Formula Used:

Mass percentage in solution = Total Salt/Total Solution × 100

Calculation:

Quantity of salt = 33g

Quantity of water = 320 g

The total quantity of solution,

⇒ 33 + 320 = 353 g

Now by using the formula,

Percentage of salt in the solution

⇒ (33/353) × 100 = 9.35% (approx)

∴ Mass percentage of the solution is 9.35 %.

Given:

In an election A got 55% of the total votes and the remaining votes were casted to B. If 10,000 votes of A are given to B, there would have been a tie

Formula used:

A got a% votes and B got b% votes, difference in the votes = (a - b) % of Total votes

Calculation:

Let the total votes be 100x

A Gets = 55x

B gets = 45x

Given that 10,000 votes of A given to B

As per question

⇒ 55x – 10,000 = 45x + 10,000

⇒ x = 2000

Total votes polled = 100x

⇒ 100 × 2000 = 200000

∴ Total votes polled is 200000

Given:

There were two candidates in an election, 10% of voters did not vote and 48 votes were found invalid. The winning candidate got 53% of the total votes and won by 304 votes.

Concept used:

Percentage

Calculation:

Let the total number of voters be 100x

10% of voters did not vote 

Number of voters who vote = 100x - 10x = 90x

48 votes were found invalid

Valid votes = 90x - 48

Votes gained by the winning candidate = 

Votes gained by the loosing candidate = 90x - 48 - 53x

⇒ 37x - 48

As per the question,

⇒ 53x - (37x - 48) = 304

⇒ 16x = 304 - 48

⇒ 16x = 256

⇒ x = 16

∴ Total number of voters = 100x = 1600
Alternate Method:

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.

Given:

65% of a number is more than 25% of the number by 120.

Calculations:

Let the number be x

According to question, (65x/100) - (25x/100) = 120

⇒ (65x - 25x)/100 = 120

⇒ 40x/100 = 120

⇒ x = (120 × 100)/40 = 300

But we have to find 20%, so (20/100) × 300 = 60

∴ The required number is 60.
Shortcut Trick:

65% - 25% = 120

⇒ 40% = 120

⇒ 20% = 60

∴ The required number is 60

Given:

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

Calculation:

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%

Given:

Out of two numbers, 65% of the smaller number is equal to 45% of the larger

number. If the sum of two numbers is 2574

Calculation:

Let the smaller number be ‘x’ and the larger number be ‘y’

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

Given:

Average is 280.

Formula used:

Average = sum of the observation/number of the observation     

Calculation:

Let the number be x

According to the question,

⇒ (x + 50% of x + 25% of x)/3 = 280

⇒ (x + x/2 + x/4)/3 = 280

⇒ 7x/12 = 280

⇒ x =  480

∴ The number is 480.

Given:

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

Calculation:

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.
Shortcut Trick:

Let us go by options.

The difference between the numbers is 22 in all cases.

So, now check the next statement.

121 = 0.55 × (121+ 99) 

That is, as the first option itself satisfies the condition and since we do no have a combination of answers, it is the solution.

∴ The required numbers are 121 and 99.

Calculation:

Let the initial oranges with the fruit seller be x.

1st selling = 0.45x + 1

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

2nd selling = 1/5 × (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

3rd 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 = 5.28/0.044 = 120

∴ The number of oranges was 120. 

C's income = Rs.2000

20% of C's income = Rs.400

10%ofB′sincome = 20%of  C′s  income

or, 10% of B's income = 400

or, B's income = Rs.4000

15% of B's income = 15% of 4000 = Rs.600

5% of A's income = 15% of B income = 600

Thus, A's income = Rs.12000

Total income of A + B + C = 12000 + 4000 + 2000

= Rs.18,000

Given:

Wood A worth Rs. 440000, Wood B worth Rs. 230000 and Wood C worth Rs. 190000

Company had to pay 15% duty on Wood A, 9% on Wood B and 7% on Wood C

Calculation:

Total duty on three woods = 440000 × 15% + 230000 × 9% + 190000 × 7%

= 440000 × 0.15 + 230000 × 0.09 + 190000 × 0.07

= 66000 + 20700 + 13300

= 100000

Answer is Rs. 100000

Given:

The number is 125.

Solution:

Given number is 125

∵ y is 10% more than 125:

So y = 125 × ( 110 / 100 )

⇒ y = 137.5

∵ x is 10 % lesser than y :

So x = 137.5 × (90 / 100)

⇒ x = 123.75 

Hence the correct answer is "123.75".

Given:

Population of A : B : C = 4 : 5 : 6 (in the beginning of 2020)

Percentage increase in the population of A : B : C = 7 : 5 : 9

Population of city 'C' (in 2021) - Population of city 'C' (in 2020) = 27000

Population of A : B (in the beginning of 2021) = 108 : 125

Calculation:

Let the population of city 'A', 'B' and 'C' was 7x, 5x and 9x (in the beginning of 2020)

And the percentage increase in the population of cities = 7y%, 5y%, and 9y%.

ATQ, 6x × [(100 + 9y)/100] - 6x = 27000 ...(i)

Again (4x) × [(100 + 7y)/100]/(5x) × [(100 + 5y)/100] = 108/125

⇒ (100 + 7y)/(100 + 5y) = 27/25

⇒ 40y = 200

⇒ y = 5

Using (i)

⇒ 6x × 145% - 6x = 27000

⇒ x = 10000

Population of city A (in 2020) = 4x = 40000

Population of city B (in 2020) = 5x = 50000

Population of city C (in 2020) = 6x = 60000

The sum of the increase in the population of all the cities together = 35% × 40000 + 25% × 50000 + 45% × 60000 = 53500

Hence, the correct answer is 53500.

Monthly income of a person was Rs. 36,000.

25% on food = (25/100) × 36000 = 9000 Rs.

12 % on his children's education = (12/100) × 36000 = Rs. 4320

x% in bank account = (x/100) × 36000 = 360x

Remaining amount = Rs. 2160.

So, we can write the above as:

9000 + 4320 + 360x + 2160 = 36000

360x = 36000 - 15480 = 20520

⇒ x = (20520/360) = 57%

The sum of amount which he saves in his bank = (57/100) × 36000 = Rs. 20520