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 mth  term of first  A.P. be equal to the nth term of the second A.P. then 2 , 5 , 8 ,….50 terms series  13 , 5 ,7 , …., 60 terms series 2  Common series  5 , 11, 17 , ….., 11940th term of series  1= 59th  term of series 2 = 119 = last term of common series ⇒  an=5+(n−1)d⇒119+1=6n⇒n=20. ∴        number of common terms are 20.