Question

A musical fountain show was organized in a park, during which 36% of the tickets were issued as half-tickets and 52% were issued as full tickets out of a total of 1500 tickets. The number of half-tickets and full-tickets issued is,
(a) 1420 and 300
(b) 540 and 78
(c) 54 and 780
(d) 540 and 780

Answer 1

Hint: The percentage term is always written as the number itself divided by 100. Therefore, 36% can be written as $\dfrac{36}{100}$in the terms of the fraction. Further, multiplying the term by the total number of tickets will give the answer. In this case, the total number of tickets is 1500.

Complete step-by-step answer:
It is given that 36% of the tickets were issued as half tickets.
36% means out of 100, 36 tickets were issued as half tickets but we know that there are in total 1500 tickets.
Therefore, out of 1500, we get,
Tickets issued as half tickets $=\dfrac{36}{100}\times 1500$ .
Simplifying the above equation, we get,
Tickets issued as half tickets = 540 tickets…………………...(i)
Similarly, we can calculate for full tickets.
It is given that 52% of the tickets were issued as full tickets.
52% means out of 100, 52 tickets were issued as full tickets but we know that there are in total 1500 tickets.
Therefore, out of 1500, we get,
Tickets issued as half tickets $=\dfrac{52}{100}\times 1500$ .
Simplifying the above equation, we get,
Tickets issued as half tickets = 780 tickets…………………...(ii)
From equation (i) and (ii),
The number of tickets issued to half tickets and full tickets are 540 and 780 tickets respectively.
Hence, option (d) is the correct option.

Note: The number of half tickets and full tickets are calculated from 1500 tickets. So, the summation of these tickets will never go above 1500. Therefore, option (a) is automatically eliminated as the sum of both the tickets turns out to be 1720 which is greater than 1500 tickets. There are approximately about 50% of the tickets as full tickets, therefore, the number of tickets must be close to half of the total number of seats which is $\dfrac{1500}{2}=750$. Therefore, option (b) is eliminated as the number is not close to be considered.