A box contains 70  marbles of different colours i.e. purple, pink and blue. Find the number of pink marbles in the box, if probability of picking up a purple marble is \(\frac{3}{7}\)and that of either a purple or a pink marble is \(\frac{4}{7}\).

10

Probability of picking a purple marble = \(\frac{No.\;of\;purple\;marbles}{Total\;number\;of\;marbles}\) 

Probability of picking a purple marble = \(\frac{3}{7}\)

⇒ \(\frac{3}{7}\) =  \(\frac{No.\;of\;purple\;marbles}{70}\) 

No. of purple marbles = 30

Probability of picking either a purple or pink marble = \(\frac{4}{7}\)

Probability of picking either a purple or pink marble =   

\(\frac{No.\;of\;purple\;or\;pink\;marbles}{Total\;No.\;of\;marbles}\) 

Let number of pink marbles= x

∴  \(\frac{x\;+\;30}{70}\) =  \(\frac{4}{7}\)

⇒ x = 10   

Hence, option D is correct.