The average marks obtained by 100 candidates in an examination is 50.Find how many candidates have passed in the examination,if the average marks of candidates who passed is 70 and that of failed candidates is 20.90756058

Let's denote the number of candidates who passed as P and the number of candidates who failed as F. We know that P + F = 100 (total number of candidates).

We also know that the average marks of all candidates is 50, which means that the total marks of all candidates is 50 * 100 = 5000.

The average marks of the candidates who passed is 70, so the total marks of the candidates who passed is 70 * P.

The average marks of the candidates who failed is 20.90756058, so the total marks of the candidates who failed is 20.90756058 * F.

Since the total marks of all candidates is the sum of the total marks of the candidates who passed and the total marks of the candidates who failed, we can write the equation:

70P + 20.90756058F = 5000.

We now have a system of two equations:

P + F = 100, 70P + 20.90756058F = 5000.

We can solve this system of equations to find the values of P and F.

First, multiply the first equation by 20.90756058 to get 20.90756058P + 20.90756058F = 2090.756058.

Subtract this equation from the second one to get 49.09243942P = 2909.243942.

Divide both sides by 49.09243942 to get P = 59.2.

Since P must be an integer, we round 59.2 to the nearest whole number, which is 59.

Substitute P = 59 into the first equation to get 59 + F = 100, which gives F = 41.

So, 59 candidates have passed and 41 candidates have failed.