Question

 A picture hall has seats for 820 persons. At a recent film show, one

usher guessed it was ¾ full, another that it was 2/3 full. The ticket

office reported 648 sales. Which usher (first or second) made the

better guess?

Answer 1

Given:

A picture hall has seats for 820 persons

At a recent film show, one  usher guessed it was ¾ full, another that it was 2/3 full

The ticket office reported 648 sales

To find:

Which usher (first or second) made the  better guess?

Solution:

Total no. of seats in the hall = 820

Total no. of seats sold were = 648

Guess made by the first usher:

1st usher guessed → $\frac{3}{4}th$ of the seats were sold

∴ No. of tickets sold in the hall as per the guess of the 1st usher is,

= $\frac{3}{4} \times 820$

= $3 \times 205$

= $\bold{615}$

Guess made by the second usher:

2nd usher guessed → $\frac{2}{3}th$ of the seats were sold

∴ No. of tickets sold in the hall as per the guess of the 2nd usher is,

= $\frac{2}{3} \times 820$

= $\frac{1640}{3}$

= $\bold{546.67}$

From the above calculations, we can see that

1st usher → 648 - 615 = 33

and

2nd usher → 648 - 546.67 = 101.33

∴ Conclusion:

• The difference between the guess and the actual no. of the sale in case of 1st usher is minimum as compared to the 2nd usher.
• Therefore, the first usher guessed closer to the actual no. of sales.

Thus, $\boxed{\bold{\underline{First \:usher}\:made\:the\:better\:guess.}}$

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some tickets of rs200 and some of rs100, of drama in a theatre were sold. The number of ticket rs200 sold was 20 more than then the number of tickets of rs100. the total amaount recived by theatre by sale of tickets was rs37000. Find the number of rs100 tickets sold.

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Answer 2

Answer:

Total number of seats = 820 Sale of total tickets = 648 Number of sold tickets guessed by first usher = 3/4 of 820 = 3/4 x 820 = 615 Number of sold tickets guessed by second usher = 2/3 of 820 = 2/3 x 820 = 1640 = 546.66 ≈ 547 Since, 615 is more close to 648 than 547.