Problem 1 :
The denominator of a fraction exceeds the numerator by 5. If 3 be added to both, the fraction becomes 3/4. Find the fraction.
Solution :
Let x be the numerator.
Given :The denominator of the fraction exceeds the numerator.
Then, the required fraction is
x/(x + 5) ----(1)
Given : If 3 be added to both, the fraction becomes 3/4.
(x + 3)/(x + 5 + 3) = 3/4
Simplify and solve for x.
(x + 3 )/(x + 8) = 3/4
4(x + 3) = 3(x + 8)
4x + 12 = 3x + 24
x = 12
To get the required fraction, substitute 12 for x in (1).
(1)-----> x/(x + 5) = 12/(12 + 5)
x/(x + 5) = 12/27
So, the required fraction is 12/27.
Problem 2 :
In a school, there are 450 students in total. If 2/3 of the total strength are boys, find the number of girls in the school.
Solution :
Given : Total no. of students in the school is 450 and 2/3 of the total strength is boys.
Then, no. of boys in the school is
= 450 ⋅ 2/3
= 300
Out of the total students 450, there are 300 boys.
Then no. of girls is
= 450 - 300
= 150
So, the numbers girls in the school is 150.
Problem 3 :
The width of the rectangle is 2/3 of its length. If the perimeter of the rectangle is 80 cm. Find its area.
Solution :
Let x be the length of the rectangle.
Then, width of the rectangle is
= 2x/3
Given : Perimeter = 80 cm.
2(l + w) = 80
Divide both sides by 2.
l + w = 40
Substitute x for l and 2x/3 for w.
x + 2x/3 = 40
(3x + 2x)/3 = 40
5x = 120
Divide each side by 5.
x = 24
2x/3 = 2(24)/3 = 16
Therefore, length and width of the rectangle are 24 cm and 16 cm.
Area of the rectangle is
= l ⋅ w
= 24 ⋅ 16
= 384 square cm.
So, the area of the rectangle is 384 square cm.
Problem 4 :
A chemist mixed 20 percent of 6.36 grams of one compound with 60 percent of 2.48 grams of another compound. How many grams were there in the mixture?
Solution :
Quantity taken from the first compound is
= 20% of 6.36
= 0.2 ⋅ 6.36
= 1.272
Quantity taken from the first compound is
= 60% of 2.48
= 0.6 ⋅ 2.48
= 1.488
Total quantity of mixture is
= Quantity from 1st comp + Quantity from 2nd comp
= 1.272 + 1.488
= 2.76
So, the quantity of the mixture is 2.76 grams.
Problem 5 :
David buys 3 pens where the price of each pen is $1.5 and the 4 pencils where the price of each pen is $0.75. If he gets a discount of 10% in the total bill, how much does he have to pay?
Solution :
First, find the total bill.
Total bill = (3 ⋅ 1.5) + (4 ⋅ 0.75)
= 4.5 + 3
= $7.5
Given : Discount is 10%.
The money that he has to pay is
= 90% of the total bill
= 0.9 ⋅ 7.5
= 6.75
So, David has to pay $6.75.
Problem 6 :
Joseph earned $24.60 for working 6 hours. How much will earn, if he works for 7.5 hours?
Solution :
Given : Money earned in 6 hours is $24.60.
Then, money earned in 1 hour is
= 24.60 / 6
= $4.10
Therefore money earned in 7.5 hours is
= 7.5 ⋅ 4.10
= $30.75
So, money earned in 7.5 hours is $30.75.
Problem 7 :
A pipe is 76.8 meters long. What will the greatest number of pieces of pipe each 8 meters long that can be cut from this pipe?
Solution :
The original length of the pipe is 76.8 meters.
The length of each pipe piece is 8 meters.
No of pieces where each piece has length 8 meters is
= 76.8/8
= 9.6
So, the greatest number of pieces of pipe each 8 meters long is 9.
Problem 8 :
The cost of a toy is $22.5. If the profit is 20%, what is the selling price of the toy?
Solution :
The cost of a toy is $22.5.
If the profit is 20%, then the selling price is 120% of cost price.
Selling price = 120 % of cots price
Selling price = 1.2 ⋅ 22.5
Selling price = 27
So, the selling price of the toy is $27.
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Nov 21, 22 10:22 AM
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