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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