The average of marks obtained by S1 and S2 is 35 more than the overage of marks obtained by S2 and S3. If the marks obtained by S3 is 75, then what are the marks obtained by S1?

Let the marks obtained by S1, S2 and S3 be $$M_1$$, $$M_2$$ and $$M_3$$ respectively.

According to the statement,

average of S1 and S2 $$-$$ average of S2 and S3 $$= 35$$

That is, $$\dfrac{M_1 + M_2}{2} - \dfrac{M_2 + M_3}{2} = 35$$

Combine the two fractions over the common denominator 2:

$$\dfrac{M_1 + M_2 - M_2 - M_3}{2} = 35$$

Simplify the numerator:

$$\dfrac{M_1 - M_3}{2} = 35$$

Multiply both sides by 2:

$$M_1 - M_3 = 70$$

The question tells us the marks of S3: $$M_3 = 75$$.

Substitute $$M_3 = 75$$ into the equation $$M_1 - M_3 = 70$$:

$$M_1 - 75 = 70$$

Add 75 to both sides:

$$M_1 = 70 + 75 = 145$$

Therefore, the marks obtained by S1 are 145.

Option D which is: 145