two forces A and B have resultant R1 ,if B is doubled the resultant R2 is at right angle to A then

a)R1=A

b)R1=B

c)R2=A

d)R2=B

R2 be the resultant of A and 2B makes an angle $\theta$ with  A
x-component of A is A
x-component of 2B is 2$B\cos \left(\theta \right)$
But here resultant is along Y-axis. Thus x-components of the resultant is zero.
$$\begin{gathered} A+2B\cos \left(\theta \right)=0 \\ \cos \left(\theta \right)=\frac{-A}{2B} \\ Resul\tan tofAandBisR1 \\ R1=\sqrt{A^2+B^2+2AB\cos \left(\theta \right)} \\ R1=\sqrt{A^2+B^2+2AB\left(\frac{-A}{2B}\right)}=B \end{gathered}$$
Option (b) is correct.