What number must be added to each of the numbers 8, 13, 26 and 40 so that the numbers obtained in this order are in proportion?

Let the number which is added to make the numbers 8, 13, 26, 40 are in proportion = $$x$$

$$=$$>  8+$$x$$, 13+$$x$$, 26+$$x$$, 40+$$x$$ are in proportion

$$=$$>  $$\frac{8+x}{13+x}=\frac{26+x}{40+x}$$

$$=$$>  $$\left(8+x\right)\left(40+x\right)=\left(26+x\right)\left(13+x\right)$$

$$=$$>  $$320+8x+40x+x^2=338+26x+13x+x^2$$

$$=$$>  $$320+48x=338+39x$$

$$=$$>  $$48x-39x=338-320$$

$$=$$>  $$9x=18$$

$$=$$>  $$x=2$$

$$\therefore\ $$The number which is added to make the numbers 8, 13, 26, 40 are in proportion = 2

Hence, the correct answer is Option B