For a certain concert, the price of balcony tickets was exactly half the price of orchestra tickets. The ratio of balcony to orchestra tickets sold was 3:2. What was the price of one orchestra ticket?

(1) the total revenue taken in from tickets of both kinds was $4200

(2) the difference between the number of balcony tickets sold and the number of orchestra tickets sold was 40


Kudos for a correct solution.
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1st Statement:
balcony tickets cost was half of the orchestra tickets, so if the count ratio is 3:2 then the cost ratio is 3:4
by this we can calculate total earnings from each type,
but not value of a individual ticket
hence not sufficient
2nd statement:
by this statement we can get the exact number of tickets for each type but we dont know the total cost, hence not sufficient

by combining both we can provide exact answer , hence answer is C
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For a certain concert, the price of balcony tickets was exactly half the price of orchestra tickets. The ratio of balcony to orchestra tickets sold was 3:2. What was the price of one orchestra ticket?

(1) the total revenue taken in from tickets of both kinds was $4200

(2) the difference between the number of balcony tickets sold and the number of orchestra tickets sold was 40


Kudos for a correct solution.
Solution

When we talk about revenue - there has to be fixed number in terms of no of unit and price per unit .
given price of orchestra tickets = x
and price of balcony tickets = x/2
ratio of balcony to orchestra tickets sold was 3:2

Required :the price of one orchestra ticket ??

St 1 : total revenue given =4200
Revenue = (x/2) 3 + (x)2
Note ratio of balcony to orchestra tickets sold was 3:2 ...no specific number given hence it is not possible to cal the the price of one orchestra ticket .

St 2: the difference between the number of balcony tickets sold and the number of orchestra tickets sold was 40
3y-2y=40
y =40

But not sufficient to cal the the price of one orchestra ticket . As price not given .

Together 1 and 2
we have both number of ticket and total revenue . Hence we can calculate the price of price of one orchestra ticket .

hence C
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Hi
As asked by you,
"What is the correct approach to resolve ambiguity between:
B = 1/2 * O or 2B = O ... (1)
or
ratio of B:O = 1:2 .... (2) "

there is no ambiguity both equations are perfectly correct, but it is quite cumbersome to solve equations.

So it is recommended that when ratio is given, like in this question.
Ration of Balcony/Orchestra = 1/2, hence if balcony tickets = x, orchestra is 2x.

Now you can proceed.

Refer the explanation provided above, @hemavakvade has provided a lucid explanation.
If you don't get the explanation, feel free to tag me again.



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