The number of terms common between the two series    2 + 5 + 8 + …up to 50 terms and the series   3 + 5 + 7 + 9 + ….up to 60 terms.

Let $m^{th}$  term of first  A.P. be equal to the $n^{th}$ term of the second A.P. then

2 , 5 , 8 ,….50 terms series  1

3 , 5 ,7 , …., 60 terms series 2 

Common series  5 , 11, 17 , ….., 119

${40}^{th}$ term of series  $\text{1}={\text{ 59}}^{\text{th}}$  term of series 2 = 119 = last term of common series

$\Rightarrow$  $a_n=5+\left(n-1\right)d\Rightarrow 119+1=6n\Rightarrow n=20.$

$\therefore$        number of common terms are 20.