Aptitude - Percentage - Discussion

GIVEN,
Easy solution with proper logic.
-> <8 = 20% OF TOTAL STUDENTS
-> EQUAL TO 8 = 48 STUDENTS
-> >8 = 2/3OF 48 --->32

Let total be x
x - (32+48)=x of 20/100,
x - 80=x of x/5,
5x - 400= x
4x = 400.
x = 400.

Given 20%(x) = below 8 years.
above 8 years = 2/3(8 years),
= 2/3(48),
= 32.
Now 48 + 32 + 20%(x) = x
80 + 20/100(x) = x.
4x = 400.
x = 100.

No.of students of 8 yrs - 48.
No.of students of above 8 yrs - 2/3 of 8 yrs old stud.
So, 2/3*48 = 32.
Total students of 8 yrs and above 8 yrs = 48 + 32 = 80 students.

Now, out of the total students, only 20% of them are below 8 years old. We don't know how many are total students yet. So let's assume the total students as X.
Students below 8 years old -X*20/100(20% is written as 20/100).
= 20x/100.

Total students in school,
80(8yr & above 8 yr total) + 20x/100(below 8yrs total) = x(total students in school that we assumed as x).
80 + 20x/100 = x.
//Take LCM for 80+20x/100.
(8000+20x)/100 = x.
//Bring the denominator 100 to the right side to multiply with x.
8000 + 20x = 100x.
8000 = 80x.
x = 100.

x is a total number of students. Then According to the question,
x = 48 + 2/3*48 + 20% of x,
x = 48 + 32 + x/5,
4x/5 = 80,
x = 100 (total number of students).

Hi, guys.

Let the total number of students be "x".

Condition 1 -> below 8 years of age = 20/100 of x = x/5 ---->1.
Condition 2 -> 8 year of age = 48 --->2.
Condition 3 -> above 8 years of age = 2/3(48) = 32 ---->3.

Then 1 + 2 + 3.
x/5 + 48 + 32 = x.
80 = x - x/5,
80 = 5x-x/5,
80 = 4x/5,
400 = 4x,
x= 400/4 =100.

If 20 % = above 8 years so , 80 % = below 8 years + exact 8 years.
therefore 80 % ----> 2/3 of 48=32 (below 8 years) + 48(exact).
80% ---------> 80.
100% ---------> 100.
So, ans = 100.

Below 8 years is 20%.
Above 8 and equal to 8 years is 80%.

The number of students above 8 years of age is 2/3 of the number of students of 8 years of age which is 48.

1/3 of 48 students is 16.
2/3 of the students are 32.
1/3+2/3 = 48 (8 years).
16 students (above 8 years),
48 + 32 = 80 equal and above 8 years,
80% = 80 then,
20% = 20.
Total 100 students.

@All.
Here is my solution.

Total Number of Students = X.
Less than 8 Years age Students = 20 % of X = (20/100) * X.
8 Years Age Students = 48,
c = (2/3) * 48 = 32.

Total Number of Students = X = Less than 8 Years age Students + 8 Years Age Students + 8 Years Age Students
X = (20/100) * X + 48+32.
X = (20/100) * X + 80.
X = (20X+8000)/100.
100X = 20X+8000.
80X = 8000.
X = 8000/80.
Total Number of Students = X= 100.

Thank you everyone.

Thank you all for explaining it.