Explanation:

Correct option 3: 33(1/3) %
Given:
Navya buys:

Half the toys at 12 for Rs 9

The other half at 18 for Rs 9

She sells all the toys at 18 for Rs 15

Let’s assume she buys LCM of 12 and 18 = 36 toys of each type, so 72 toys in total.

Step 1: Cost Price (CP)
For 36 toys at 12 for Rs 9:

12 toys = Rs 9 → 36 toys = Rs 9 × (36 ÷ 12) = Rs 27

For 36 toys at 18 for Rs 9:

18 toys = Rs 9 → 36 toys = Rs 9 × (36 ÷ 18) = Rs 18

Total CP = Rs 27 + Rs 18 = Rs 45

Step 2: Selling Price (SP)
She sells all 72 toys at 18 toys for Rs 15:

18 toys = Rs 15 → 72 toys = Rs 15 × (72 ÷ 18) = Rs 15 × 4 = Rs 60

Step 3: Profit/Loss
SP = Rs 60

CP = Rs 45

Profit = Rs 60 – Rs 45 = Rs 15

Step 4: Profit %=(CP/Profit))×100

= (15/45)x100 = 33.33%
Navya gains 33.33% on the transaction.