**Understanding percents worksheet :**

Worksheet on understanding percents is much useful to the students who would like to practice solving real world problems involving percents.

1. What is 20% of 50 ?

2. If A's salary is 20% less than B's salary. By what percent is B's salary more than A's salary ?

3. In an election, a candidate who gets 84% of votes is elected by majority with 588 votes. What is the total number of votes polled ?

4. When the price of a product was decreased by 10 % , the number sold increased by 30 %. What was the effect on the total revenue ?

5. A student multiplied a number by 3/5 instead of 5/3. What is the percentage error in the calculation ?

6. A student multiplied a number by 3/5 instead of 5/3. What is the percentage error in the calculation ?

7. If there are 3 boys and 7 girls in a class then, what percent of the class is made up of boys ?

8. There are 15 boys and 12 girls in a section A of class 7. If 3 boys are transferred to section B of class 7,then find the percentage of boys in section A.

9. A sells to B an item at 15% profit. B sells the same item to C at 20% profit. If C pays $ 1656 for it. What is the price at which A bought the item?

10. If good are purchased for $ 1500 and one fifth of them sold at a loss of 15%. Then at what profit percentage should the rest be sold to obtain a profit of 15%?

11. I purchased 120 books at the rate of $3 each and sold 1/3 of them at the rate of $4 each. 1/2 of them at the rate of $ 5 each and rest at the cost price. Find my profit percentage.

12. A trader marks his goods 20% above the cost price and allows a discount of 10% for cash. Find the profit percentage

13. A person wants to get 20% profit after selling his object at 20% discount. Find the required percentage increase in marked price.

14. A person buys 8 articles for $15 and sells them at 10 for $18. Find the profit or loss percentage.

15. Difference between the cost price of two products is $10. Difference between the selling price is $20. If one is sold at 20% profit and other one is sold at 20% loss, find the cost price of each product.

**Problem 1 :**

What is 20% of 50 ?

**Solution :**

20 % of 50 = 0.2 x 50 = 10

**Hence, 20% of 50 is 10**

**Problem 2 :**

If A's salary is 20% less than B's salary. By what percent is B's salary more than A's salary ?

**Solution :**

Let us assume B's salary = $ 100 ----------(1)

Then, A's salary = $ 80 --------(2)

Now we have to find the percentage increase from (2) to (1).

Difference between (1) and (2) = $ 20

Percentage increase from (2) to (1) = (20/80) x 100% = 25%

**Hence, B's salary is 25% more than A's salary. **

**Problem 3 :**

In an election, a candidate who gets 84% of votes is elected by majority with 588 votes. What is the total number of votes polled ?

**Solution :**

Let "x" be the total number of votes polled.

Given : A candidate who gets 84% of votes is elected by majority of 476 votes

From the above information, we have

84% of x = 588 ---------> 0.84x = 588

x = 588 / 0.84 = 700

**Hence, the total number of votes polled 700.**

Let us look at the next problem on "Understanding percents worksheet**"**

**Problem 4 :**

When the price of a product was decreased by 10 % , the number sold increased by 30 %. What was the effect on the total revenue ?

**Solution :**

Before decrease in price and increase in sale,

Let us assume that price per unit = $ 100.

Let us assume that the number of units sold = 100

Then the total revenue = 100 x 100 = 10000 -----------(1)

After decrease 10 % in price and increase 30 % in sale,

Price per unit = $ 90.

Number of units sold = 130

Then the total revenue = 90 x 130 = 11700 -----------(2)

From (1) and (2), it is clear that the revenue is increased.

Difference between (1) and (2) = 1700

Percent increase in revenue

= (Actual increase / Original revenue) x 100 %

= (1700/10000) x 100 %

= 17 %

**Hence, the net effect in the total revenue is 17 % increase. **

Let us look at the next problem on "Understanding percents worksheet**"**

**Problem 5 :**

A student multiplied a number by 3/5 instead of 5/3. What is the percentage error in the calculation ?

**Solution :**

In the given two fractions, the denominators are 5 and 3.

Let assume a number which is divisible by both 5 and 3.

Least common multiple of (5, 3) = 15.

So, let the number be 15.

15 x 3/5 = 9 ----------(1) ---------incorrect

15 x 5/3 = 25 ---------(2) --------correct

Difference between (1) and (2) is 16

Percentage error = (Actual error / Correct answer ) x 100 %

= (16 / 25) x 100 %

= 64 %

**Hence, the percentage error in the calculation is 64 %. **

Let us look at the next problem on "Understanding percents worksheet**"**

**Problem 6 :**

A student multiplied a number by 3/5 instead of 5/3. What is the percentage error in the calculation ?

**Solution :**

In the given two fractions, the denominators are 5 and 3.

Let assume a number which is divisible by both 5 and 3.

Least common multiple of (5, 3) = 15.

So, let the number be 15.

15 x 3/5 = 9 ----------(1) ---------incorrect

15 x 5/3 = 25 ---------(2) --------correct

Difference between (1) and (2) is 16

Percentage error = (Actual error / Correct answer ) x 100 %

= (16 / 25) x 100 %

= 64 %

**Hence, the percentage error in the calculation is 64 %. **

Let us look at the next problem on "Understanding percents worksheet**"**

**Problem 7 :**

If there are 3 boys and 7 girls in a class then, what percent of the class is made up of boys ?

**Solution :**

Total number of students in the class = 3 + 7 = 10

Percentage of boys = (No. of boys / Total no. of students) x 100 %

= (3 / 10) x 100 %

= 30 %

**Hence, 30 % of the class is made up of boys **

Let us look at the next problem on "Understanding percents worksheet"

**Problem 8 :**

There are 15 boys and 12 girls in a section A of class 7. If 3 boys are transferred to section B of class 7,then find the percentage of boys in section A.

**Solution :**

**Before transfer :**

No. of boys in section A = 15

No. of boys in section B = 12

**Given :** 3 boys are transferred from section A to B

**After transfer :**

No. of boys in section A = 12

No. of boys in section B = 12

**Hence, percentage of boys in section A is 50%**

Let us look at the next problem on "Understanding percents worksheet**"**

**Problem 9 :**

A sells to B an item at 15% profit. B sells the same item to C at 20% profit. If C pays $ 1656 for it. What is the price at which A bought the item?

**Solution :**

**Hence, the price at which A bought the item is $1200 **

Let us look at the next problem on "Understanding percents worksheet"

**Problem 10 :**

If good are purchased for $ 1500 and one fifth of them sold at a loss of 15%. Then at what profit percentage should the rest be sold to obtain a profit of 15%?

**Solution :**

As per the question, we need 15% profit on $1500.

Selling price for 15% on 1500

S.P =115% x 1500 = 1.15x1500 = **1725**

**When all the good sold, we must have received $1725 for 15% profit.**

When we look at the above picture, in order to reach 15% profit overall, the rest of the goods ($1200) has to be sold for $1470.

That is,

C.P = $1200, S.P = $1470, Profit = $270

Profit percentage = (270/1200) x 100

Profit percentage = 22.5 %

**Hence, the rest of the goods to be sold at 22.5% profit in order to obtain 15% profit overall.**

Let us look at the next problem on "Understanding percents worksheet"

**Problem 11 :**

I purchased 120 books at the rate of $3 each and sold 1/3 of them at the rate of $4 each. 1/2 of them at the rate of $ 5 each and rest at the cost price. Find my profit percentage.

**Solution :**

Total money invested = 120x3 = $360 -------(1)

Let us see, how 120 books are sold in different prices.

From the above picture,

Total money received = 160 + 300 +60 = $ 520 --------(2)

Profit = (2) - (1) = 520 - 360 = $160

Profit percentage = (160/360)x100 % = 44.44%

**Hence the profit percentage is 44.44**

Let us look at the next problem on "Understanding percents worksheet"

**Problem 12 :**

A trader marks his goods 20% above the cost price and allows a discount of 10% for cash. Find the profit percentage

**Solution :**

Let the cost price be $100.

Then, marked price (M.P) = $120

Let the selling price be "X"

From the above picture, we get

90% of (M.P) = X

(0.9).120 = X

108 = X --------> S.P = 108

Cost price = $100, Selling Price = $108 ---------> **Profit % = 8%**

Let us look at the next problem on "Understanding percents worksheet"

**Problem 13 :**

A person wants to get 20% profit after selling his object at 20% discount. Find the required percentage increase in marked price.

**Solution :**

Let the cost price be $100.

Then, the selling price = $120

Let the marked price be "X"

From the above picture, we get

80% of (M.P) = S.P

(0.8)X = 120

X = 150 --------> M.P = 150

Cost price = $100, Marked Price = $150

**Hence, the required percentage increase = 50%**

Let us look at the next problem on "Understanding percents worksheet"

**Problem 14 :**

A
person buys 8 articles for $15 and sells them at 10 for $18. Find the profit or loss percentage.

**Solution :**

**Cost price : **

8 articles -------> $15

40 articles = 5 x 8 articles = 5x15 = $75

**C.P of 40 articles = $75 ----------(1)**

**Selling price :**

10 articles -------> $18

40 articles = 4 x 10 articles = 4(18) = $72

**S.P of 40 articles = $72 ----------(2)**

From (1) and (2), we get C.P > S.P.

So there is loss.

And loss = (1) - (2) = 75 - 72 = 3

Loss percentage = (3/75)x100 % = 4%

**Hence, the loss percentage is 4. **

Let us look at the next problem on "Understanding percents worksheet"

**Problem 15 :**

Difference between the cost price of two products is $10. Difference between the selling price is $20. If one is sold at 20% profit and other one is sold at 20% loss, find the cost price of each product.

**Solution :**

Let "x" and "y" be the cost prices of two products.

Then, x - y = 10 --------(1)

Let us assume thatr "x" is sold at 20% profit

Then, the selling price of "x" = 120% of "x"

selling price of "x" = 1.2x

Let us assume thatr "y" is sold at 20% loss

Then, the selling price of "y" = 80% of "y"

selling price of "x" = 0.8y

Given : Selling price of "x" - Selling price of "y" = 12

1.2x - 0.8y = 20 -------> 12x - 8y = 200

3x - 2y = 50 --------(2)

Solving (1) and (2), we get x = 30 and y = 20

**Hence, the cost prices of two products are $30 and $20.**

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