The number of Bollywood movies released of actor X increased by 75% from the year 2017 to 2018, while that of actor Y decreased by 66.67% from the year 2017 to 2018. If the total number of mov￾ies released of both the actors decreased by 10% from the year 2017 to 2018, then find the ratio of their number of movies released in the year 2017?
Answers
Given:
(I) The number of Bollywood movies released of actor X increased by 75% from the year 2017 to 2018.
(ii) For actor Y, it decreased by 66.67% from the year 2017 to 2018.
(iii) The total number of movies released of both the actors decreased by 10% from the year 2017 to 2018.
To find:
(I) The ratio of their movies released in 2017.
Solution:
Let the number of movies released by X in 2017 be x and by Y be y.
Given,
the number of movies increased by 75% from 2017 to be 2018.
In 2018, the number of movies released by X
= (100+75)% of x
= 175% of x
= 1.75x
For Y it decreased by 66.67% by 2017 to 2018, so the number of released by Y in 2018 are
= (100-66.67)% of y
= 33.33% of y
= 0.3333y
Total movies released by them in 2017 is (x+y)
Given that they decreased by 10% in 2018.
So, in 2018, they are:
(100-10)% of (x+y)
= 90% of (x+y)
= 0.9(x+y)
This is equal to (1.75x + 0.3333y)
So,
0.9x + 0.9y = 1.75x + 0.3333y
=> 0.8x = 0.566y
=> x/y = 1.41
So, the ratio of movies released by X and Y is 1.41