Percentage - MCQ 1 Solved MCQs GATE ME General Aptitude

Solution:

Assume the total number of students is 100:

• 60% of the students are boys, so:
• Boys: 60
• Girls: 40
• Number of girls who scored more than 40 marks:
• 80% of girls = 80% of 40 = 32
• Number of students who scored more than 40 marks:
• 60% of total students = 60
• Therefore, the number of boys who scored more than 40 marks:
• 60 - 32 = 28
• Number of boys who scored 40 marks or less:
• Total boys - Boys (scored more) = 60 - 28 = 32
• Fraction of boys who scored 40 marks or less:
• 32/60 = 8/15

 Let the total number of voters be x.
- Voters who did not cast votes: 0.10x
- Total voters who cast ballots: 0.90x
The winner received 47% of all voters:
- Winner's votes: 0.47x
Let the loser's votes be y. According to the problem:
- Winner got 308 more votes than the rival:
0.47x = y + 308
y = 0.47x - 308
Total valid votes (winner + loser) plus blank votes equal total ballots cast:
0.47x + (0.47x - 308) + 60 = 0.90x
Simplify the equation:
0.94x - 248 = 0.90x
0.04x = 248
x = 248 / 0.04 = 6200
Thus, the number of voters on the list is 6200.

Let the original salary of Deepak = 100

Correct hike = 50%
Correct new salary = 100 + 50 = 150

By mistake, hike given = 80%
Salary paid = 100 + 80 = 180

Excess payment per month
= 180 − 150 = 30

Excess payment for 3 months
= 30 × 3 = 90

Correct salary for 4th month
= 150 − 90 = 60

Percentage of correct new salary received in 4th month:

Let the price of two articles are 3X and 4X.
After increment the ratio will be:
110% of 3x/(4X+4) = 3/4
x=10
Thus the CP of second article = 4X = 4*10 = Rs. 40.

Solution:

Assuming a total of 100 students in the school:

• The ratio of boys to girls is 3:2, which means:
• Boys: 60
• Girls: 40
• 20% of boys receive scholarships:
• 60 boys × 20% = 12 boys
• 25% of girls receive scholarships:
• 40 girls × 25% = 10 girls
• Total students who receive scholarships:
• 12 boys + 10 girls = 22 students
• Percentage of students who do not receive scholarships:
• 100% - (22 students / 100 students × 100%) = 78%

Total amount = x
Savings(%)
[100 – (23 + 33 + 19 + 16 )]% = 9 %
9% of x = 504
=> x = 504 * 100/9 = 5600
Amount spend on food and insurance policy together = 56% of 5600 = Rs.3136

Assume the total amount is Rs.100.

Deepika reserves 15% for auto fare, which amounts to Rs.15.

This leaves her with Rs.85.

The cost of 70 oranges is Rs.85, meaning:

• Cost of 35 oranges is calculated as follows:

Cost of 35 oranges = (Rs.85 / 70) * 35 = Rs.42.50.

After buying the oranges, the remaining amount for apples is Rs.42.50.

The cost for 40 apples is Rs.85, leading to:

• Cost of X apples can be calculated using:

Cost of X apples = Rs.42.50.

Thus, X = (Rs.85 / Rs.42.50) * 40 = 20 apples.

Therefore, if Deepika buys 35 oranges, she can buy 20 more apples.

Price of the car: Rs. 4,50,000

The car was insured for 80% of its price. In case of a complete loss, the insurance company paid 90% of the insured amount. Here’s how to calculate the difference:

• Calculate the insured amount: Insured Amount = Rs. 4,50,000 × 80% = Rs. 3,60,000
• Calculate the amount received from insurance: Amount Received = Rs. 3,60,000 × 90% = Rs. 3,24,000
• Determine the difference between the price of the car and the amount received: Difference = Rs. 4,50,000 − Rs. 3,24,000 = Rs. 1,26,000

The final difference is Rs. 1,26,000.

Solution:

Let's assume Arun’s motorcycle consumes 1 litre of petrol per day. This means the tank capacity is 10 litres.

With a 25% increase in usage each day, the new daily consumption becomes:

• 1 litre + (25% of 1 litre) = 1 litre + 0.25 litres = 1.25 litres per day.

The number of days the petrol will last can be calculated as follows:

• Days = Total capacity / Daily usage = 10 litres / 1.25 litres = 8 days.

Last year, there were 610 boys in a school. This year, the number decreased by 20 percent.

To find the current number of boys:

• Calculate 20 percent of 610: 0.2 × 610 = 122
• Subtract this from the original number: 610 - 122 = 488

Now, to find the number of girls:

• The number of girls is 175 percent of the total number of boys:
• Calculate 175 percent of 488: (175/100) × 488 = 854

Thus, the total number of girls in the school is 854.

Hence. option(B) is correct

The maximum marks per paper in 3 subjects in Mathematics, Physics, and Chemistry are set in the ratio 1 : 2 : 3.

Giri's scores in each subject are as follows:

• Mathematics: 40% of 1
• Physics: 60% of 2
• Chemistry: 35% of 3

To find the overall percentage, we calculate:

• Mathematics contribution: 0.4 (40% of 1)
• Physics contribution: 1.2 (60% of 2)
• Chemistry contribution: 1.05 (35% of 3)

The total marks obtained is:

Overall % = 100 × (0.4 + 1.2 + 1.05) / (1 + 2 + 3)

This simplifies to:

Overall % = 100 × (2.65) / 6 = 44.16%

Thus, Giri's overall percentage is 44%.

passed in science = 50%
passed in social = 75%
20% students failed in both the subjects and 80% passed in at least one subject
No of students passed in both subjects = 50+75−x=80  x=45% 45% of x = 270  x = 270*100/45 = 600
Total number of students =600

Solution:

The weight of water in 300 kg of dry fruits is calculated as follows:

• Water content = 20% of 300 kg = 60 kg
• Weight of the fruit alone = 300 kg - 60 kg = 240 kg

To find the total weight when fresh:

• In fresh fruits, 25 kg of fruit corresponds to 100 kg of total weight.
• Using this ratio: Total fresh weight = (100 * 240) / 25 = 960 kg.

Let the total number of individuals involved in the election be x.

The percentage of those who did not vote is calculated as follows:

• 100 - (35 + 42) = 23%

The difference between the number of votes for Person B and those who did not vote is:

• 42% of x - 23% of x = 570

This simplifies to:

• 19% of x = 570

To find x, we can rearrange the equation:

• x = 570 * 100 / 19 = 3000

Therefore, the total number of participants in the college election is 3000.

Solution:

To find the percentage of non-defective products, we need to calculate the contribution of each bulb type:

• L1: Produces 20% of products, with 3% defective:
• Non-defective = 20% × (1 - 0.03) = 20% × 0.97 = 19.4%
• L2: Produces 15% of products, with 7% defective:
• Non-defective = 15% × (1 - 0.07) = 15% × 0.93 = 13.95%
• L3: Produces 32% of products, with 2% defective:
• Non-defective = 32% × (1 - 0.02) = 32% × 0.98 = 31.36%

Now, we sum the non-defective contributions:

Total non-defective percentage = 19.4% + 13.95% + 31.36% = 64.71%

Thus, the percentage of non-defective products is 64%.

1. otal students = 500

2. Boys = 65% of 500 = 0.65 × 500 = 325
   Girls = 500 – 325 = 175

3. Boys who failed = 40% of 325 = 0.40 × 325 = 130
   Girls who failed = 20% of 175 = 0.20 × 175 = 35

4. Total failures = 130 + 35 = 165
   Total passes = 500 – 165 = 335

Total increase in population is calculated by adding the annual growth rate to the additional growth rate:

• Annual growth rate: 6%
• Additional growth due to rural development: 2%
• Total growth rate: 6% + 2% = 8%

The percentage increase over two years can be found using the formula for compound interest:

• First year increase: 8%
• Second year increase: 8% of the new population (1 + 0.08) = 1.08
• Overall increase calculation: Population after 2 years = (1.08)² = 1.1664

This results in a total percentage increase of:

• Percentage increase: (1.1664 - 1) × 100 = 16.64%

Thus, the percentage increase in the population after two years is 16.64%.

Let Gugan’s salary = G
Let Harish’s salary = H

Step 1: Form equations
G + H = 30000

After increment:

• Gugan → 1.05G
• Harish → 1.07H

1.05G + 1.07H = 31800

Step 2: Substitute
G = 30000 - H
1.05(30000 - H) + 1.07H = 31800

Step 3: Solve
31500 - 1.05H + 1.07H = 31800
31500 + 0.02H = 31800
0.02H = 300

Hence, option(B) is correct

• Percentage passed in at least one subject = 70 + 55 − 40 = 85
• Percentage failed in both = 100 − 85 = 15