# 100 seats in a theater. @5/tkt; 1rs/ tkt and rs 0.05/ tkt. Adding tptalnto 100 rs.

+1 vote
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Here it goes:
A theatre has the capacity of 100 seats. Ticket prices are: Adult male - Rs.5; Adult female - Re.1 and Child - Re. 0.05 (5 praise). On a certain day the show was housefull and the collection was exactly Rs.100.
How many males, females and children were there? (All were not females.)

posted Jun 26, 2016

+1 vote

Since all are not female we have to include both male and children to the audience as one could quickly check in the case of 95 female and 1 male we have 100 rupees but 4 seats are still vacant.

If we are to include children then there has to be at least 20 of them or their multiples. It can be observed here that the price is most sensitive to the number of males and least to the children.
So we can have high number of children without much impact on the price. By that logic we can pick the highest allowed number for children ie.,
Children ------ 80 ------- 4 rupees
Now I will make up for price gap created by high children count with as many as males as possible without exceeding the 100 price limit ie.,
Male ------ 19 ------ 95 rupees
Now it's clear that 1 rupee is in the balance so finally
Female -------- 1 ------- 1 rupee.
This is how they are split in the theatre.

Excellent reasoning.  Weldone!

19 men = 19 x 5 = 95 Rs
1 woman = 1 rupee
80 children = 80 x 0.05 = 4 rupees
total persons = 100
total fare = 100 rs

answer Feb 9, 2017 by anonymous

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