Question

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?

Answer 1

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 = $$5x = 5 \times 30 = 150$$.