Word Problems on Percentage 1 :
This is the continuity of our web content given on "Word problems on Percentage".
Before we look at the problems, if you want to know the shortcuts required for solving percentage problems,
Problem 1 :
A student multiplied a number by 3/5 instead of 5/3. What is the percentage error in the calculation ?
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 ⋅ 3/5 = 9 ----- (1) -----> incorrect
15 ⋅ 5/3 = 25 -----(2) -----> correct
Difference between (1) and (2) is 16
Percentage error is
= (Actual error / Correct answer) ⋅ 100 %
= (16 / 25) ⋅ 100 %
= 64 %
Hence, the percentage error in the calculation is 64 %.
Problem 2 :
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.
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%
Problem 3 :
If there are 3 boys and 7 girls in a class then, what percent of the class is made up of boys ?
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 %
Hence, 30 % of the class is made up of boys.
Problem 4 :
Two numbers are respectively 20% and 50% are more than a third number, Find the the ratio of the two numbers.
Let x be the third number.
the first number = (100+20)% of x = 120% of x = 1.2x
the first number = (100+50)% of x = 150% of x = 1.5x
First no. : Second no. = 1.2x : 1.5x
Multiply both the terms of the ratio by 10.
First no. : Second no. = 12x : 15x
Divide both the terms of the ratio by 3x.
First no. : Second no. = 4 : 5
Hence, the ratio of the two number is 4 : 5.
Problem 5 :
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.
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 any triangle = 180°
Then, we have
x + 1.2x + 0.8x = 180°
3x = 180°
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°.
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