In an examination a student Raj got 25% of the maximum marks and faile...
Given:
- Raj got 25% of maximum marks and failed by 15 marks.
- Ravi scored 35% of maximum marks which was 25 marks more than passing marks.
To find: The necessary percentage required for passing.
Solution:
Let's assume that the maximum marks for the exam is 'M' and the passing marks is 'P'.
According to the given information,
Raj scored 25% of M and failed by 15 marks.
So, we can write an equation as:
25/100 * M = P - 15
Ravi scored 35% of M, which is 25 marks more than the passing marks.
So, we can write another equation as:
35/100 * M = P + 25
We need to find the percentage required for passing, which is (P/M) * 100.
To solve for P, we can use elimination method:
- Multiply the first equation by 35 and the second equation by 25.
- Subtract the second equation from the first equation.
This gives us:
(25/100 * 35 * M) - (35/100 * 25 * M) = (P - 15) * 35 - (P + 25) * 25
Simplifying the above equation, we get:
-1500 = -10P + 350
-1850 = -10P
P = 185
Therefore, the passing marks is 185 out of maximum marks M.
To find the necessary percentage required for passing, we can substitute P = 185 in the first equation and solve for (P/M) * 100:
25/100 * M = 185 - 15
M = 800
(P/M) * 100 = (185/800) * 100 = 23.125 ≈ 28.75%
Therefore, the necessary percentage required for passing is 28.75%.
Hence, option (c) is the correct answer.