how-to-solve-percentage

How to Solve Percentage Problems

You might have noticed two different sale labels on two different shops on the same item. Like one offers a 50% discount, and the other offers a 60% discount with a minor difference in MRP. Let’s take an example of it:

Shop A offers a 50% discount on Rs 500 items, and shop B offers a 60% discount on Rs 600 items. You might be attracted to the Shop A offer because it has less MRP and a nice % discount. Wait, do you know that Shop B offers a much better offer. How? Let’s know it with understanding about how to solve percentage problems? 

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Calculation of MRP of shop A:

You can see that Shop A sells the item at a 50% discount on MRP of 500 Rs that means 500 x (50/100) = 250. Now, subtract 250 from the original MRP, that is, 500 – 250 = 250. It means Shop A offers the item at 250 Rs.

Calculation of MRP of shop B:

You can see that Shop B sells the item at a 60% discount on MRP of 600 Rs that means 600 x (60/100) = 360. Now, subtract 360 from the original MRP, that is, 600 – 360 = 240. It means Shop B offers the item at 240 Rs.

This implies that shop B offers the item on the less MRP. Now, you can understand how important it is to know the percentage concept. Don’t know how to solve percentage problems? Do not worry; we have mentioned all the necessary details about how to solve percentage problems. Let’s check all the details and save more money.

What is the percentage?

In mathematics, the percent or percentage is the ratio or the number expression that is denoted as a fraction of 100. In Latin, it means ” by a hundred.” 

It is denoted using the symbol “%.” But the abbreviations used to denote percentage are “pct,” “pct.” and “pc”. Moreover, the percentage is the pure number that does not have any dimension and unit of measurement.

The basic percentage formula is:

basic percentage formula

Is it important to learn about percentage?

Yes, it is! There are several applications where the concept of percentage is used, such as:

Shopping: Sale is the major factor of shopping where the percentage’s concept is used. Like there is a 25% discount on the 100 Rs item. It means the item will be sold at the MRP of 75.

Packed food nutrients: You have noticed that the packed food items have a % table at the packet’s backside. It denotes how many percent the particular nutrient has in the food with respect to the 100 like a pickle has 20% sodium. This denotes that if you take 1 teaspoon of pickle, it has 1/5 of sodium of overall nutrient elements.

Cell phone battery usage: Suppose you have to visit out of the station and you check your cell phone battery that shows only 10% battery value. It means that you need to charge it before living from home. Otherwise, it will not last long, even upto 1 hour.

The interest rate offered by the bank: When you deposit or borrow money from the bank, it always declares a certain interest rate on the money. If you deposit $ 5,000/ year and the bank offers a 7% interest rate per year. It means that you will get the $350 interest at the end of the year, and your amount will be $5,350.

Apart from this, there are several applications where the concept of percentage is used. Therefore, it is always worthy of learning the concept of percentage. So, now let’s understand the method to solve percentage problems.

How to solve percentage problems?

Key points:

The percentage is always 100. So we find out the percentage of any number from 100 percent.
Always know that 100% is absolute, so 100 percent of any number is always the whole number.
For example, 100% of 10 numbers is 10; similarly, 100 % of 20 numbers is 20.

The next point to learn on how to solve percentage problems is that if you have to find the 50 % of any number, you just have to divide it by 2 only if you find 50 % (that is 50/100 is always 1/2).
Let’s understand it through an example-

Suppose students have to find out the 50% of the 70 is 70/2 = 35

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Another example can be 50 % of 60 = 60 /2 = 30.

As the 50 percent of any number is half similarly, the 25% of any number shall be 1/4. So you have to divide by 4 to find the one-fourth of any number.

Let’s take another point, suppose you have to find out the 20% of any number then it will always be one-fifth of the number. So if you have to find the 20 % of 80 thus, it will be as follows –

80 x 1/5 = 16.

Follow the following steps to solve the percentage problems:

  1. Determine the whole or the total amount.
  2. Divide the amount to express it as a percent. In maximum cases, you need to divide the smaller amount by the higher amount.
  3. Multiply the result with 100.

Let’s take an example of it:

Suppose you have 60 marbles. 15 of those marbles are red; what percent of all marbles are red?

Solution:

  1. The obtained value is 15, and the maximum value is 60.
  2. As per the given formula:

The number of red marble = (15/60) x 100

(1/4) x 100 = 25%

It means that you have 25% red marbles.

Let’s take one more example of it:

Suppose you bought an item of price $6.00, and you paid $7.00. Calculate the sales tax rate of the city? 

We know that the sales tax might be a certain percentage of the original price, so let’s figure out the actual tax. The actual tax was:

7.00 – 6.00 = 1.00

Now, the sales tax would be a percentage of the cost:

1.00 = (x)(6.00)

Solving the value of x, you will get:

1.00 ÷ 6.00 = x = 0.1666666 = 16.666%

The sales tax rate was 16.66%.

Let’s understand percentages with more practice questions!

Example 1:

Suppose we have a question in which you need to find out the 60 percent of 200. Let’s understand it through examples – 

So firstly you must learn that percentage is written as % and it means per one hundred.

Thus we write 60 percent of 200 as follows – 

60 % of 200 

= (60 /100) x 200

Example 2 :

Now let’s take another example. Suppose students have a question that you have got 40 marks out of 80, so now you have to find out what is the percentage of 40 marks out of 80 marks.

Let’s learn how to solve percentage problems by the x method. 

So let’s take the answer is X. 

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So we will have the equation – 

X% of 80 = 40 

(X / 100) x 80 = 40 

40/80 = X/100

X =  100 x 40/ 80 

X = 4000/80 

X = 50 

Thus the answer is 50%.

Example 3:

Let’s take another high-level example – 

Suppose students have to compute your grades for your course as follows – 

5% for attendance10 % for assignments85% for the final exam

Suppose you have scored the following – 

80 marks in attendance70 marks in assignments95 marks in final exams

This is a more tough situation in how to solve percentage problems. Follow the following steps-

Firstly you have to write all the percentages in decimals, so we all know that we need to divide the number of percentage by 100 as the percent means 100 thus, you will do the following

5 % = 5/100 = 0.0510 % = 10/100 = 0.1085 % = 75/100 = 0.85

So the next step is to add all these decimals, and if you add these decimals, you will get 100 as the answer because the percentage is always 100.

The next step in how to solve percentage problems is to multiply the score with respective decimals. Follow the given equation – 

Let’s take the answer as Z.

Z = 0.05 x 80 + 0.1 x 70 + 0.85 x 95 

= 4 + 8 + 80.75

= 92.75 

Thus the total marks in the percentage you have got is 92.75.

Conclusion

Percentage problems are the easiest mathematical problem. But still, many students face difficulty in solving percentage problems because they fail to understand the concept. But if you follow the above-mentioned steps and ways, and you easily solve the problems. We hope this blog would have helped you solve all kinds of percentage problems. If you are still struggling with percentages homework queries or any other math problems, you can contact our expert panel anytime and resolve all your queries. Get the best math homework help from the experts.

Frequently Asked Questions

How do you calculate percentages quickly?

To find the given percent decimal form, you need to move the decimal to the two places right. For instance, you can write a decimal form of 10% as 0.1. If you calculate what 10% of is, say, 300 seniors, you can multiply the seniors’ number by 0.1.

How do you find 3%?

To calculate 3% of $2,000. First, you can take it as 0.03 × $2,000. Then multiply the number 3 × $2,000 = $6,000. Finally, put the decimal two places from the right: $60.00.

What is percentage of a number?

In math, a percentage is a ratio or number, which describes a fraction of 100. The symbol “%” denotes percent. For example, 45% is equivalent to the decimal point 0.45, or 45/100.

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