A man purchase of 120 exercise books at rate of ₹30 each and sold $\frac{1}{3}rd$ of them at rate of ₹40 each, $\frac{1}{2}$ of them at the rate of ₹50 each and the rest at cost price his profit percentage was :

$44\frac{4}{9}$%

Total cost price of 120 books = 120 × 30 = 3600

$\frac{1}{3}rd$ of the books sold  at rate of ₹40 each

Selling price of these books = \(\frac{1}{3}\) × 120 × 40

= 1600

$\frac{1}{2}rd$ of the books sold  at rate of ₹50 each

Selling price of these books = \(\frac{1}{2}\) ×120 × 50

= 3000

Remaining books = 120 - 40 - 60 = 20

Selling price of these remaining books = Cost price of these books

Total selling price of remaining 20 books = 20 × 30 = 600

Total selling price of 120 books = 1600 + 3000 + 600

= 5200

Profit percent = \(\frac{5200 - 3600}{3600}\) × 100%

= \(\frac{1600}{3600}\) × 100%

= \(\frac{4}{9}\) × 100%

The correct answer is option (2) : $44\frac{4}{9}$%