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A theatre runs for a total of 12 hrs in a day. During any particular week a total of 2 movies are to be played. If one movie is played 3 times and other two times ¼ of the time is left unused, in the other hand if the other movie is played 3 times and the first 2 times all the time is used. What is the duration of each movie in minutes?

A theatre runs for a total of 12 hrs in a day. During any particular week a total of 2 movies are to be played. If one movie is played 3 times and other two times ¼ of the time is left unused, in the other hand if the other movie is played 3 times and the first 2 times all the time is used. What is the duration of each movie in minutes? Correct Answer 216, 54

Let the duration of movies be X and Y

3X + 2Y = 12 – (¼ ) × 12

⇒ 3X + 2Y = 9       ---- (1)

2X + 3Y = 12       ---- (2)

5Y = 18

Y = (18/5) × 60 = 216 mins

X = /2 = 54 mins

∴ The duration of each movie in minutes = 216, 54

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