In an examination, the number of those who passed and failed are in the ratio of 2:3. If 5 more appeared and 5 less passed, the ratio of passes to failures would be 1:2. Find how many students appeared for exam?
Question
In an examination, the number of those who passed and failed are in the ratio of 2:3. If 5 more appeared and 5 less passed, the ratio of passes to failures would be 1:2. Find how many students appeared for exam?
Solution
Let's solve this step by step:
Step 1: Let's assume the number of students who passed the exam is 2x and the number of students who failed is 3x. So, the total number of students who appeared for the exam is 2x + 3x = 5x.
Step 2: According to the problem, 5 more students appeared for the exam and 5 less passed. So, the new number of students who passed is 2x - 5 and the new number of students who failed is 3x + 5.
Step 3: The problem states that this new situation creates a ratio of passes to failures of 1:2. So, we can set up the equation (2x - 5) / (3x + 5) = 1 / 2.
Step 4: Solving this equation for x gives x = 15.
Step 5: Substituting x = 15 into the equation from step 1 gives the total number of students who appeared for the exam as 5x = 5*15 = 75.
So, 75 students appeared for the exam.
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