Problem 1 :
A product is sold for $96 with a profit of 20%. Find the cost price of the product.
Problem 2 :
If the profit is 10%, then the selling price is $132. If the profit is 15%, what must be the selling price?
Problem 3 :
A student multiplied a number by ⅗ instead of ⁵⁄₃. What is the percentage error in the calculation?
Problem 4 :
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.
Problem 5 :
If there are 3 boys and 7 girls in a class then, what percent of the class is made up of boys?
Problem 6 :
Two numbers are respectively 20% and 50% are more than a third number, Find the the ratio of the two numbers.
Problem 7 :
In a triangle, the first angle is 20% more than the third angle. Second angle is 20% less than the third angle. Then find the three angles of the triangle.
Problem 8 :
A trader cheats his customer to make a profit by stating that he sells at cost price but gives his customers only 800 grams. for every 1000 grams. What is his profit percentage?
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, find the price at which A bought the item.
Problem 10 :
Mr. Lenin sold a chair at a loss of 15%. If he had sold at a profit of 10%, he would have got $100 more. What is the cost is the cost price of the chair?
Problem 11 :
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%?
Problem 12 :
By selling 20 articles, a trader gained the selling price of 5 articles. Find the profit percent.
1. Answer :
Let x be the cost price of the product.
Given : When the profit is 20%, the selling price is $96.
(100 + 20)% of x = 96
120% of x = 96
1.2x = 96
Divide both sides by 1.2
x = 80
The cost price of the product is $80.
2. Answer :
To answer this question, first we have to know the cost price of the product.
Let x be the cost price.
Given : When the profit is 10%, the selling price is $120.
(100 + 10)% of x = 132
110% of x = 132
1.1x = 132
Divide each side by 1.1.
x = 120
The cost price of the product is $120.
If the profit is 15%, then the selling price is
= (100 + 15)% of the cost price
= 115% of the cost price
= 1.15 ⋅ 120
= 138
When the profit is 15%, the selling price is $138.
3. Answer :
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 ⅗ = 9 ----(1) ----> incorrect
15 x ⁵⁄₃ = 25 ----(2) ----> correct
Difference between (1) and (2) is 16.
Percentage error is
= (Actual error/Correct answer) ⋅ 100%
= (16/25) ⋅ 100%
= 64%
4. Answer :
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%.
5. Answer :
Total number of students in the class :
= 3 + 7
= 10
Percentage of boys is
= (No. of boys/Total no. of students) ⋅ 100%
= ³⁄₁₀ ⋅ 100 %
= 30%
6. Answer :
Let x be the third number.
First number :
= (100 + 20)% of x
= 120% of x
= 1.2x
Seocnd number :
= (100 + 50)% of x
= 150% of x
= 1.5x
Ratio between the first number and second number :
= 1.2x : 1.5x
Multiply both the terms of the ratio by 10 to get rid of the decimal point.
= 12x : 15x
Divide both the terms of the ratio by 3x.
= 4 : 5
7. Answer :
Let x be the third angle.
First angle = 120% of x
= 1.2x
Second angle = 80% of x
= 0.8x
Sum of the three angles in a triangle = 180°
x + 1.2x + 0.8x = 180°
3x = 180°
Divide both sides by 3.
x = 60°
First angle :
= 1.2(60°)
= 72°
Second angle :
= 0.8(60°)
= 48°
Hence, the three angles of the triangle are 72°, 60° and 48°.
8. Answer :
Cheated Value = 1000 - 800 = 200.
False weight = 800.
Profit percemntage :
= (Cheated value/False weight) ⋅ 100%
= (²⁰⁰⁄₈₀₀) ⋅ 100%
= 0.25 ⋅ 100%
= 25%
9. Answer :
Hence, the price at which A bought the item is $1200.
10. Answer :
Let x be the cost price of the chair.
S.P (-15%) = 85% of x
= 0.85x ----(1)
S.P (+10%) = 110% of x
= 1.1x ----(2)
In (2), he got $100 more than (1).
(2) - (1) = 100
1.1x - 0.85x = 100
0.25x = 100
25x = 10000
Divide both sides by 25.
x = 400
Hence, the cost price of the chair is $400.
11. Answer :
As per the question, we need 15% profit on $1500.
Selling price for 15% on 1500.
S.P = 115% ⋅ 1500
= 1.15 ⋅ 1500
= 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 ⋅ 100%
= 0.225 ⋅ 100%
= 22.5%
Hence, the rest of the goods to be sold at 22.5% profit in order to obtain 15% profit overall.
12. Answer :
Let x be the seling price of 5 articles.
Selling price of 20 articles :
= 4 ⋅ (selling price of 5 articles)
= 4 ⋅ x
= 4x
Given : Profit of 20 articles = Selling price of 5 articles.
Profit of 20 articles = x
Cost price of 20 articles :
= Selling price of 20 articles - Profit of 20 articles
= 4x - x
= 3x
Profit percentage :
= ˣ⁄₃ₓ ⋅ 100%
= ⅓ ⋅ 100%
≈ 33.33%
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