Percentage - MCQ 3 - Railways 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:

• 21600 = P₀( 1.20)³
• 21600 = P₀( 12/10 x 12/10 x 12/10)
• hence, P₀ = 12500

• 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 in seats = 8%
• Increased percentage in price = 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 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