A student has to obtain 35% of the total marks to pass. He got 25% of the total marks and failed by 80 marks. The total of marks is :

1. 400

2. 800

3. 600

4. 750

Given:

Passing marks = 35% of the total marks

A candidate gets = 25% of the total marks

The candidate fails by = 80 marks

Let $x$ be the maximum marks.

∴ Passing marks = $\dfrac{35}{100} \times x$

= $\dfrac{7}{20}\times x$

= $\dfrac{7x}{20}$ ……….(1)

A candidate gets = $\dfrac{25}{100} \times x$

= $\dfrac{1}{4}\times x$

= $\dfrac{x}{4}$

Since the candidate got $\dfrac{x}{4}$ marks and fails by 80 marks. Hence, we can say that passing marks = $\Big(\dfrac{x}{4} + 80\Big)$ marks.

Using equation (1), we get,

∴ $\dfrac{7x}{20} = \dfrac{x}{4} + 80$

⇒ $\dfrac{7x}{20} - \dfrac{x}{4} = 80$

LCM of 20 and 4 is 20,

∴ $\dfrac{7x}{20} - \dfrac{5x}{5\times4} = 80$

⇒ $\dfrac{7x}{20} - \dfrac{5x}{20} = 80$

⇒ $\dfrac{(7 - 5)}{20} \times x = 80$

⇒ $\dfrac{2}{20} \times x = 80$

⇒ $x = \dfrac{80 \times 20}{2}$

⇒ $x = \dfrac{1600}{2}$

⇒ $x = 800$

Hence, option 2 is the correct option.