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प्रश्न
In an examination, the ratio of passes to failures was $$4 : 1$$. Had 30 less appeared and 20 less passed, the ratio of passes to failures would have been $$5 : 1$$. How many students appeared for the examination?
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उत्तर
Let the number of passes be $$4x$$ and failures be $$x$$.
Total students appeared = $$4x + x = 5x$$.
In the second case:
Number of students appeared = $$5x - 30$$
Number of students passed = $$4x - 20$$
Number of failures = Total appeared – Total passed
$$= (5x - 30) - (4x - 20)$$
$$= x - 10$$
The new ratio of passes to failures is $$5 : 1$$: $$\frac{4x - 20}{x - 10} = \frac{5}{1}$$
Cross-multiply: $$4x - 20 = 5(x - 10)$$
$$4x - 20 = 5x - 50$$
$$5x - 4x = 50 - 20$$
$$\implies x = 30$$
Total students who appeared = $$5x = 5 \times 30 = 150$$.
