Using weighted avgs:

50% of the tickets are at 50% profit,
40% of rest 50% are at 10% profit i.e. 20% are at 10% profit
and leftover 30% are at 80% loss.

We need to find the avg profit/loss

\(Cavg = \frac{(+50)*50 + (+10)*20 + (-80)*30}{50 + 20 + 30}\)

\(Cavg = \frac{300}{100}\)

\(Cavg = 3\)% profit
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Let us say,

Total tickets = 100 nos

Price per ticket = $1, so price of 100 tickets = $ 100

First selling = 50% of tickets at 50% profit :

50% of 100 at 50 % profit =50 + 25 = $ 75

Remaining tickets = 50 nos

Second selling = 40% of 50 at 10% profit :

20 + 2 = $ 22

Remaining tickets = 30 nos

Third selling = 30 tickets at 80% loss :

30*0.2 = $ 6

Total = 75 +22 + 6 = $ 103

Original price = $ 100

Therefore 3 % profit (D)
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Let us consider each ticket costs 100 units and there are a total of 100 tickets.
1. 50% tickets at 50% profit :
Cost of each ticket = 100 + 50 = 150
Total Tickets sold at above price = 50
Total amount from sale = 150 * 50 = 7500

2. 40% of remaining at 10% profit:

Cost of each ticket = 100 + 10 = 110
Total tickets sold at above price = 40% of remaining = 40% of 50 = 20
Total amount from sale = 20 * 110 = 2200

3. Remaining sold at 80% loss:
Cost of each ticket = 100 – 80 = 20
Total tickets at above price = 100 – 50 – 20 = 30
Total amount from sale = 20 * 30 = 600

Total Cost Price of tickets = 100 * 100 = 10000
Total Selling Price = 7500 + 2200 + 600 = 10300
Total Profit % = (10300-10000)/10000% = 3%

Hence D is the correct answer.

Let there be total 100 tickets at 100$ each .

so : ( 50*150)+(20*110)+(30*20)
= 10300
profit= 10300-10000= 300 $ % gain , 3% option D

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Soluton:
assume number of tickets=10
Price of each ticket=100
So total price=10*100=1000

Step1: 50% tickets sold at 50% profit

so 50% profit on each ticket =150,
So sp of 5 tickets=5*150=750

Step 2: 40% of left sold at 10% profit
40% of left=40/100 * 5=2

profit=110
so total sp of 2 tickets=2*110=220

Step 3: Remaining tickets were 3 which were sold at 80% loss
so means they were sold for (100-80)=20

so sp for 3=3*20=60

Now sum all the sp=750 + 220 +60=1030

so profit=1030-1000/1000 *100

30/1000 *100=3 %

Hope clear!!
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