Something based on Perentage.

Question

A candidate who gets 20% marks in an examination fails by 30 marks but another candidate who gets 32% gets 42 marks more than the passing marks. Then the percentage of pass marks is:

1. 52%
2. 50%
3. 33%
4. 25%

Answer 1

Passing marks = 20% of x + 30 ....(1)

As he needs 30 more marks wo added.

Passing marks = 32% of x - 42 .....(2)

As he has 42 more marks then passing so subtracted.

From (1) and (2)

20% of x + 30 = 32% of x - 42

32% of x - 20% of x = 30 + 42

12% of x = 72

x = $\frac{72 * 100}{12}$

x = 600

So total marks 600.

From equation (1)

Passing marks = 20% of x + 30

= $\frac{20}{100}$ * 600 + 30 = 120 + 30 = 150

Passing percentage = $\frac{150}{600} * 100$ = 25%

Answer 2

If you fail at 20% and pass at 32% the percentage at which you pass is between these. Only one option satisfies this.

Otherwise solve the system:

$$ 0.2x = y - 30 \\ 0.32x = y+42 $$

and you will know everything about your problem.

And show your work next time, this is not a homework service.