Percentage - MCQ 3 - SSC CGL MCQ

Given:

A reduction of 20% in the price of rice enables a housewife to buy 5 kg more for Rs. 1200.

Calculation:

Let the original price per kg of rice be Rs. 100x.
After a 20% reduction, the new price per kg = 100x - 100x × 20%
⇒ 100x - 20x = 80x
Thus, the new price is Rs. 80x per kg.

According to the question:

The difference in the quantities of rice bought with Rs. 1200 at the old and new prices is 5 kg.
So,
New quantity − Old quantity = 5 kg

Using the price formulas:

Simplify the equation:

Now, solving for x:

Now, substitute the value of x into the new price formula:

New price = 48 Rs. per kg
Thus, the reduced price per kg of rice is Rs. 48.

We can use the formula for compound growth to find the initial population:

where:

• P is the final population (21600)
• P₀ is the initial population (what we want to find)
• r is the annual growth rate (20% or 0.20)
• n is the number of years (3)

Plug in the known values:

Simplify and solve for P₀:

Let the total number of votes in the election be x.
12% of the voters did not cast their votes, so the number of valid votes is 88% of the total votes.
Valid votes = 0.88 × x
The winner received 45% of the total votes. Therefore, the votes received by the winner are:
0.45 × x
The remaining votes are for the rival candidate, which is:
0.88x − 0.45x = 0.43x votes
The winner defeated his rival by 2000 votes. So, the difference between the winner’s votes and the rival’s votes is:
0.45x − 0.43x = 2000
0.02x = 2000
Solving for x

Let the original number be x.

1. First, the number is decreased by 25%. So, the decreased number becomes:

Decreased number = x - (25/100) x = 0.75x

2. The decreased number is then increased by 20%. So, the resulting number becomes:

Resulting number = 0.75x + (20/100)(0.75x) = 0.75x + 0.15x = 0.9x

3. The resulting number is 40 less than the original number:

x - 0.9x = 40

4. Simplifying the equation:

0.1x = 40

5. Solving for x:

x = 40 / 0.1 = 400

Thus, the original number is 400.

Given:

Reduced percentage = 8%

Increased percentage = 4%

Formula used:

Effective percentage = x - y - (xy)/100

x= increased percentage

y = Decreased percentage

Calculation:

Effective percentage = 4 - 8 - (4 × 8)/100

= - 4 - 0.32

= - 4.32%

The -ve sign means decreased percentage.

∴ The correct answer is a 4.32% decrease.

Total sweets = 30
Ratio of the sweets received by Shweta and Pallavi is 2 : 3
Let x
 be ratio coefficient.
∴ Sweets received by Shweta = 2x
And sweets received by Pallavi = 3x
Total sweets = 2x + 3x = 5x
But given
5x = 30
∴ x = 30/5  =6
∴Sweets received by Shweta = 2 × 6
= 12
and by Pallavi = 3 × 6
= 18
∴ Percentage of sweets received by Shweta =
and percentage of sweets received by Pallavi = 

= 60%

Let the original weights of A and B be A and B, respectively. Since the ratio of their weights is 1 : 2, we can say:
A = x and B = 2x
A’s weight increases by 20%, so the new weight of A is:
New weight of A = A + 20% of A = x + 0.20x = 1.2x
The total weight of A and B after the increase is 60 kg, and it is also given that the total weight increased by 30%. Therefore, the original total weight of A and B was:
Original total weight = 60/1.30 = 46.15 kg (approximately)
The original total weight of A and B is also A + B = x + 2x = 3x, so:
3 x = 46.15 ⇒ x = 46.15/3 = 15.38 kg (approximately)
So, A’s original weight is approximately 15.38 kg, and B’s original weight is:
B = 2x = 2 × 15.38 = 30.76 kg (approximately)
The new total weight is 60 kg, and the new weight of A is 1.2x = 1.2 × 15.38 = 18.46 kg. Therefore, the new weight of B is:
New weight of B = 60 − 18.46 = 41.54 kg (approximately)
Now, we can calculate the percentage increase in B’s weight:

Thus, B’s weight increased by 35%.

Let the cost price (CP) of the article be x.
The marked price (MP) is 20% higher than the cost price, so:
Marked Price (MP) = x + 20% of x = x + 0.20x = 1.2x
A discount of 20% is given on the marked price.
The selling price (SP) after the discount is:
Selling Price (SP) = MP − 20% of MP = 1.2x − 0.20 × 1.2x = 1.2x − 0.24x = 0.96x
Now, compare the selling price (SP) with the cost price (CP):
The selling price is 0.96x, and the cost price is x.
The percentage loss or gain can be calculated as:

Thus, the seller incurs a loss of 4% in this transaction.

Let the original price of rice be P (per kg).
The original consumption of rice by the family is 50 kg.
The original expenditure of the family is:
Original expenditure = 50 × P = 50P
The price of rice is increased by 30%.
The new price of rice becomes:
New price = P + 30% of P = P + 0.30P = 1.3P
The family’s expenditure increases by 20%.
The new expenditure is:
New expenditure = 50P + 20% of 50P = 50P + 0.20 × 50P =60P
Let the new consumption of rice be x kg.
The new expenditure is the product of the new price and the new consumption:
New expenditure = x × 1.3P
Set the new expenditure equal to the previous calculation of 60P:
x × 1.3P = 60P

Thus, the new consumption of the family is approximately 46 kg.

Given:

A person had Rs.4000 in his account two years ago.

In the first year he deposited 20% in his account

Next year he deposited 10% of the increased amount.

Calculation:

In the first year, 

He deposit = 20% × 4000 = Rs. 800

∴ Increased amount after 1st year = 4000 + 800 = 4800

Next year,

He deposit = 10% × 4800 = 480

∴ Total amount in the person's account after 2 years = 4800 + 480

= 5280

∴ Total amount in the person's account after 2 years = 5280

Let the total number of votes be T.
Party B gets 15,000 votes.
According to the problem, Party A secured 25% more votes than Party B. So, the number of votes for Party A is T − 15000, and it is also 25% more than Party B’s votes, which means:

Therefore, the total number of votes is 40,000.
Party A’s votes = T − 15000 = 40000 − 15000 = 25000.
Party B’s votes = 15,000 (as given).
The difference between Party A and Party B’s votes is:
25000 − 15000 = 10000
Thus, Party B loses the election by 10,000 votes.

Let the total number of apples the vendor initially had be 100 (for simplicity).
On the first day:
The vendor sells 50% of the apples:
Apples sold on day 1 = 50% of 100 = 50
The remaining apples after selling 50% are:
Remaining apples = 100 − 50 = 50
He then throws away 20% of the remaining apples:
Apples thrown away on day 1 = 20% of 50 = 10
The remaining apples after throwing away 20% are:
Remaining apples after day 1 = 50 − 10 = 40
On the second day:
The vendor sells 60% of the remaining apples:
Apples sold on day 2 = 60% of 40 = 24
The remaining apples after selling 60% are:
Remaining apples after selling on day 2 = 40 − 24 = 16
He throws away the rest, which is 16 apples.
Total apples thrown away:
Apples thrown away on day 1 = 10
Apples thrown away on day 2 = 16
Total apples thrown away = 10 + 16 = 26
Percentage of apples thrown away:

Thus, the vendor throws away 26% of his apples.

Let the total number of women be 100 (for simplicity).
Women above 30 years of age:
40% of the women are above 30 years of age, which means:
Women above 30 years = 40% of 100 = 40 women
Women less than or equal to 50 years of age:
80% of the women are less than or equal to 50 years of age, which means:
Women less than or equal to 50 years = 80% of 100 = 80 women
Women above 50 years of age:
Since 80% are less than or equal to 50 years, the remaining 20% are above 50 years of age, which means:
Women above 50 years = 20% of 100 = 20 women
Women who play basketball:
20% of all women play basketball, which means:
Total basketball players = 20% of 100 = 20 women
Women above 50 years of age who play basketball:
30% of the women above 50 years play basketball, which means:
Basketball players above 50 years = 30% of 20 = 6 women
Women less than or equal to 50 years who play basketball:
The total number of basketball players is 20, and 6 of them are above 50 years of age.
Therefore, the number of players less than or equal to 50 years of age is:
Basketball players less than or equal to 50 years = 20 − 6 = 14 women
Percentage of players who are less than or equal to 50 years of age:
Percentage of players less than or equal to 50 years = 
Thus, 70% of the basketball players are less than or equal to 50 years of age.

Total cost of items = ₹60.

Sales tax paid = 40 paise = ₹0.40.

Tax rate = 10%. So, the tax amount is 10% of the cost of taxed items (denoted as T).

The sales tax equation is:

Solving for T:

Now, the cost of tax-free items is:
Cost of tax-free items = 60 − T − Sales tax = 60 − 4 − 0.40 = 55.60 rupees.
Thus, the cost of tax-free items is ₹55.60.

Total employees = 100 (for simplicity).
Number of women = 60% of 100 = 60 women.
Number of men = 40% of 100 = 40 men.
75% of the women earn 20,000 or more:
Women earning 20,000 or more = 75% of 60 = 0.75 × 60 = 45 women.
Total number of employees earning more than 20,000 per month is 60% of the total employees:
Employees earning more than 20,000 = 60% of 100 = 60 employees.
Out of these 60 employees, 45 are women, so the remaining 15 must be men:
Men earning more than 20,000 = 15 men.
The total number of men is 40, and 15 men earn more than 20,000, so the number of men earning less than 20,000 is:
Men earning less than 20,000 = 40 − 15 = 25 men.
The fraction of men earning less than 20,000 is:
Fraction = 25/40 = 5 / 8
Thus, the correct answer is A: 5/8

Let the total number of books in the library be T.
30% of the books are in History:
History books = 30% of T = 0.30 × T
The remaining books after accounting for History are:
Remaining books = T − 0.30 × T = 0.70 × T
50% of the remaining books are in English:
English books = 50% of the remaining = 0.50 × 0.70 × T = 0.35 × T
After accounting for English books, the remaining books are:
Remaining books after English = 0.70T − 0.35T = 0.35T
40% of the remaining books are in German:
German books = 40% of the remaining = 0.40 × 0.35 × T = 0.14 × T
After accounting for German books, the remaining books are:
Remaining books after German = 0.35T − 0.14T = 0.21T
The remaining 4200 books are in regional languages, so:
0.21 × T = 4200
Solving for T:
T = 4200/0.21 = 20000
Thus, the total number of books in the library is 20,000.

Let maximum marks in the examination be 100x and passing marks be yy

A got 30% of the maximum marks, => 30x + 10=y ----------(i)

Similarly, for B = 40x − 15 = y -------(ii)

Subtracting equation (i) from (ii), => 10x = 25

=> x = 2.5

Substituting it in equation (ii), we get: Passing marks = y = 85.

Initial population = 15,000.

First year: Population increases by 10%.

New population after the first year:

Second year: Population increases by 20%.

New population after the second year:

Third year: Population decreases by 10%.

New population after the third year:

Thus, the population after 3 years will be 17,820.

The initial solution contains 30 liters, with alcohol and water in the ratio 2:3.

The amount of alcohol in the solution is:

The amount of water in the solution is:

We need to add some amount of alcohol (let it be x) to make the alcohol content 60% of the total solution.

After adding x liters of alcohol, the new total volume of the solution will be 30 + x liters, and the amount of alcohol will be 12 + x liters.

The concentration of alcohol should be 60%, so:

Solving the equation:

Thus, 15 liters of alcohol must be added to the solution.

Given,

Total number of sweets = 720

Concept:

x% of any value = Actual value × (x/100)

Calculation:

Let number of children be x, then

Number of sweets each child get = x × (20/100)

According to the question

x × x × 20/100 = 720

⇒ x²/5 = 720

⇒ x² = 720 × 5

⇒ x² = 3600

⇒ x = √3600

⇒ x = 60

∴ Number of sweets each child get is = 60/5 = 12