It has been observed that four consecutive years, the number of car manufactured by a company has been doubled over the previous year’s. If the average number of cars manufactured by the company in four years is 750, the number of cars manufactured during the fourth year will be

The correct answer is (b) 1200.

Let $x$ be the number of cars manufactured in the first year. The number of cars manufactured in the second year is $2x$, the number of cars manufactured in the third year is $2^2x=4x$, and the number of cars manufactured in the fourth year is $2^3x=8x$. The average number of cars manufactured in the four years is $750$, so we have

$$\frac{x+2x+4x+8x}{4}=750$$

Solving for $x$, we get $x=250$. Therefore, the number of cars manufactured in the fourth year is $2^3x=2^3(250)=1200$.

Option (a) is incorrect because $1000$ is not a power of $2$. Option (c) is incorrect because $1600$ is not a multiple of $4$. Option (d) is incorrect because $2000$ is not a multiple of $8$.