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Mathematics

In an examination, the ratio of passes to failures was 4 : 1. If 30 less had appeared and 20 less passed, the ratio of passes to failures would have been 5 : 1. How many students appeared for the examination?

Ratio Proportion

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Answer

Ratio of passes to failures = 4 : 1. So, the number of students passed = 4x and number of students failed = x.

Total students appeared for examination = 4x + x = 5x.

In second case, number of students appeared = 5x - 30.

Number of students passed in second case = 4x - 20.

So, number of students failed = (5x - 30) - (4x - 20) = 5x - 4x - 30 + 20 = x - 10.

According to question,

4x−20x−10=51⇒4x−20=5(x−10)⇒4x−20=5x−50⇒4x−5x=−50+20⇒−x=−30⇒x=30.\dfrac{4x - 20}{x - 10} = \dfrac{5}{1} \\[0.5em] \Rightarrow 4x - 20 = 5(x - 10) \\[0.5em] \Rightarrow 4x - 20 = 5x - 50 \\[0.5em] \Rightarrow 4x - 5x = -50 + 20 \\[0.5em] \Rightarrow -x = -30 \\[0.5em] \Rightarrow x = 30.

∴ 5x = 150

Hence, total number of students appeared for examination were 150.

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