Percentage

Anubhav's income allocations are as follows:

1. Electricity bills: 14%
2. Rent: 28%
3. Shopping: 18%

The total percentage spent from his income is:
(14% + 28% + 18%) = 60%

This means that he has 40% of his income remaining. Let's denote Anubhav's total income as X. The remaining amount is 0.4X.

We know that 1/4 of the remaining amount is Rs. 5120:
0.25 × 0.4X = 5120

Solving for X:

Now, to find the amount spent on electricity bills, which is 14% of his income:

Electricity bills = 14% of 51200

Electricity bills =

Electricity bills = Rs.

According to the question, the amount spent on electricity bills is Rs. 7160, which means there may have been a slight discrepancy in the question options. Based on calculations, the closest correct answer should indeed be Rs. 7160.

The problem requires determining the initial number of males in a town with a total population of 50,000, given percentage increases in both male and female populations and a resulting new total population.

1. Let the initial number of males be and the initial number of females be . We know:
... (Equation 1)

2. After the increase, the number of males becomes , and the number of females becomes .

3. The new total population is given as 56,000, thus:
... (Equation 2)

4. Solve the system of equations by substituting from Equation 1 into Equation 2:









Thus, the initial number of males in the town was 30,000.

To solve for the maximum marks in the examination, let's first understand the given situation: The passing mark is 300, but the student who scored 225 was said to fail by 10%. This means that the marks required to pass are 10% more than what the student scored.

Let’s denote the maximum marks by . The percentage required to pass is given by:

The percentage obtained by the student is:

According to the problem, this percentage is 10% below the passing percentage:

We can simplify this equation to find :

By clearing the fractions, we derive:

Solving for :

Dividing both sides by 10:

Thus, the correct answer is .

To solve the problem, we need to find how many students prefer neither online nor hybrid classes based on the given percentages.

1. Understanding the Concepts:

- Total students: 200
- Online class preference: 60% of 200
- Hybrid class preference: 25% of the remaining students who do not prefer online classes
- Neither: Students who prefer neither online nor hybrid classes

2. Calculate Number of Students Preferring Online Classes:

3. Calculate Remaining Students:

4. Calculate Number Preferring Hybrid Classes:

5. Calculate Number Preferring Neither:

Final Answer:

The number of students who prefer neither online nor hybrid classes is 60.

Let's determine the fraction of the salary that is left after a man has covered his expenses. We'll calculate the total fraction spent and subtract it from the whole salary.

First, the fraction spent on rent is , food is , and transportation is . The total fraction spent is:

To add these fractions, we need a common denominator. The least common multiple of 5, 4, and 10 is 20.

Convert each fraction to have a denominator of 20:

• For : Multiply numerator and denominator by 4 →
• For : Multiply numerator and denominator by 5 →
• For : Multiply numerator and denominator by 2 →

Add the fractions:

The total fraction spent is of the salary. Therefore, the fraction of the salary that is left is the remaining part of the whole:

To simplify , divide both the numerator and denominator by their greatest common divisor, which is 5:

Thus, the fraction of the salary that is left is .

To solve the problem, we need to find the overall percentage of students who fail, based on the failure rates among boys and girls and their ratio in the class.

1. Understanding the Concepts:

- Ratio: Represents a comparative value. A ratio of 3:2 means for every 3 boys, there are 2 girls.
- Percentage: A way to express a number as a part of a whole (out of 100).
- Weighted Average: Since the numbers of boys and girls are different, we need a weighted average failure rate based on their ratio.

2. Given Values:

Ratio of boys to girls = 3 : 2
Let total students = 3 + 2 = 5 parts
Assume total students = 100 (for easier calculation; you can also work in ratios). Then,
Boys = 60 (i.e., 3 parts out of 5 ⇒ 3/5 × 100 = 60)
Girls = 40 (i.e., 2 parts out of 5 ⇒ 2/5 × 100 = 40)
Failing Boys = 20% of 60 = 12
Failing Girls = 30% of 40 = 12

3. Calculating Overall Percentage of Failures:

Total failing students = 12 (boys) + 12 (girls) = 24
Total students = 100

Final Answer:

The overall percentage of students who fail is 24%.

To solve the problem, we need to determine the net effect of a price increase followed by a discount, both expressed in percentages.

1. Understanding the Concepts:

- Price Increase: An upward change in price, expressed as a percentage of the original price.
- Discount: A reduction applied after the increase, on the increased price.
- Net Change Formula: When an increase of x% is followed by a decrease of y%, the net percentage change is given by:

2. Given Values:

- Increase = 25%
- Discount = 20%

3. Calculating the Net Percentage Change:

Final Answer:

There is no net change in the price; the overall percentage change is 0%.