Olympiad Test: Comparing Quantities - Class 7 MCQ

3 computers are used by 6 students.

To determine the number of computers needed:

• Each computer serves 2 students (6 students / 3 computers).
• For 24 students, the calculation is:
• 24 students / 2 students per computer = 12 computers.

Solution:

To find the percentage of students who are present, follow these steps:

• Calculate the number of students present:
• Total students: 32
• Absent students: 8
• Present students = 32 - 8 = 24
• Calculate the percentage of present students:
• Percentage = (Present students / Total students) × 100
• Percentage = (24 / 32) × 100 = 75%

Thus, 75% of the students are present.

Solution:

The number of radios that are out of order is 16.

To find the percentage of radios that are out of order, use the following formula:

• Percentage = (Number of radios out of order / Total number of radios) × 100

Substituting the values:

• Percentage = (16 / 25) × 100 = 64%

Thus, 64% of the radios are out of order.

Solution:

To find the percentage of items that are not defective:

• First, calculate the percentage of defective items:
• Defective items: 5 out of 500
• Percentage of defective items = (5 / 500) × 100 = 1%

Next, determine the percentage of items that are not defective:

• Percentage of not defective items = 100% - 1% = 99%

To find the percentage of voters who voted yes:

• Start with the number of voters who voted yes: 90.
• Divide this number by the total number of voters: 120.
• Calculate the fraction: 90/120.
• To convert this fraction to a percentage, multiply by 100: (90/120) x 100%.
• Simplifying the fraction gives 3/4.
• Now, calculate: 3/4 x 100% = 75%.

Thus, 75% of the voters voted yes.

Total number of children: 40

Percentage of children who like football: 25%

To find the number of children who do not like playing football:

• Calculate the percentage of children who do not like football: 100% - 25% = 75%
• Now, find 75% of the total number of children:
• Number of children who do not like football = 75% of 40
• Calculation: (75/100) * 40 = 30

Therefore, 30 children do not like playing football.

Number of children that like getting wet in rain = 8% of 25
= 8/100 × 25
= 8/4
= 2 children.
Number of children that don't like getting wet in rain
= 25 - 2
= 23 children
Therefore, there are 23 such students that don't like getting wet in rain.
 

Solution:

Rahul saved Rs 20 due to a 25% discount on the sweater. To find the original price:

• Let the original price be x.
• The discount can be expressed as:
• 25% of x = Rs 20
• This translates mathematically to:
• 25/100 * x = 20
• By rearranging, we get:
• 25x = 2000
• x = 2000 / 25
• x = Rs 80

Thus, the original price of the sweater was Rs 80.

To find the number of voters who did not vote:

• Total voters in the constituency: 15,000
• Percentage of voters who voted: 60%
• Number of voters who voted: 15,000 × 60% = 9,000
• Number of voters who did not vote: 15,000 - 9,000 = 6,000

Therefore, the number of voters who did not vote is 6,000.

Meeta saves Rs 400 from her salary. If this is 10% of her salary, what is her salary?

To find Meeta's salary, we can use the following steps:

• Identify the percentage: Rs 400 is 10% of her salary.
• Set up the equation: 10% of salary (x) = 400.
• Convert percentage to decimal: 10% = 10/100 = 0.1.
• Write the equation: 0.1 * x = 400.
• Solve for x: x = 400 / 0.1.
• Calculate: x = 4000.

Therefore, Meeta's salary is Rs 4000.

Percentage of matches won: 25%

Percentage of matches lost: 100% - 25% = 75%

Number of matches lost:

• Calculate 75% of 20 matches:
• 75% of 20 = (75/100) x 20
• Result: 15 matches lost.

To calculate the percentage increase in the number of games won by the school team:

• The team won 6 games this year.
• Last year, they won 4 games.
• To find the increase in wins: 6 - 4 = 2.
• Next, calculate the percentage increase using the formula:
• Percentage Increase = (Amount of Change / Original Amount) × 100
• Substituting the values:
• Percentage Increase = (2 / 4) × 100 = 50%

The percentage increase in the number of games won is 50%.

Percentage of decrease can be calculated using the formula:

• Change in illiterate people = Initial number - Final number
• In this case: 150 lakhs - 100 lakhs = 50 lakhs

Now, apply the formula for percentage of decrease:

• Percentage of decrease = (Change in illiterate people / Original amount) × 100
• Substituting the values: (50 lakhs / 150 lakhs) × 100
• This simplifies to: (50 / 150) × 100 = 33.33%

Thus, the percentage of decrease in the number of illiterate persons is 100/3%.

Cost of an item is Rs 50. It was sold with a profit of 12%. Find the selling price.

To find the selling price (SP) when the cost price (CP) is Rs 50 and the profit is 12%, follow these steps:

• Calculate the profit amount: Profit = CP × (Profit Percentage / 100)
• Substituting the values: Profit = 50 × (12 / 100) = 6
• Now, add the profit to the cost price to find the selling price: SP = CP + Profit
• Thus, SP = 50 + 6 = Rs 56

The selling price of the item is Rs 56.

Solution:

To calculate the cost of an item after a 10% discount on the marked price of Rs 100, follow these steps:

• Determine the discount amount: 10% of Rs 100.
• Calculate the discount:
  • Discount = 10/100 × 100 = Rs 10
• Subtract the discount from the marked price:
  • Cost after discount = Rs 100 - Rs 10 = Rs 90

Thus, the final cost of the item is Rs 90.

Solution:

Chameli has Rs 600 left after spending 75% of her money. This means:

• She retains 25% of her total amount.
• Thus, 600 equals 25% of her initial amount.

To find the original amount (let's call it x), we can set up the equation:

• 25% of x = 600
• Which can be expressed as: (25/100) * x = 600

Now, solving for x:

• Multiply both sides by 4 (since 100/25 = 4):
• x = 600 * 4 = Rs 2400

Therefore, Chameli initially had Rs 2400.

Price of the scooter last year: Rs 34,000

Increase: 20%

The amount of increase can be calculated as follows:

• 20% of Rs 34,000 = Rs 6,800

To find the new price:

• New Price = Last Year Price + Amount of Increase
• New Price = Rs 34,000 + Rs 6,800
• New Price = Rs 40,800

Therefore, the current price of the scooter is Rs 40,800.

Solution:

The price of the scooter last year was Rs 34,000. This year, it has decreased by 5%. To find the current price, follow these steps:

• Calculate the amount of decrease: 5% of Rs 34,000.
• Use the formula: Decrease = (5/100) × 34,000 = Rs 1,700.
• Subtract the decrease from the original price: Rs 34,000 - Rs 1,700 = Rs 32,300.

Therefore, the current price of the scooter is Rs 32,300.

Solution:

To find the gain percentage, we can use the following steps:

• Calculate the gain by subtracting the cost price (CP) from the selling price (SP):
• Gain = SP - CP
• In this case:
• Gain = 875 - 750 = 125

Next, we calculate the gain percentage using the formula:

• Gain Percentage = (Gain / CP) × 100
• Substituting the values:
• Gain Percentage = (125 / 750) × 100
• This simplifies to:
• Gain Percentage = (1/6) × 100 ≈ 16.67%

Thus, the gain percentage is approximately 16.67%.