UNDERSTANDING PERCENTS WORKSHEET

Understanding percents worksheet :

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

Understanding percents worksheet

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.

Understanding percents worksheet - Solution

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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