In this task, you need to provide the correct option for a given problem from the provided options.

Problem: x starts a business with rs . 45000 . y joins in the business after 3 months with rs . 27000 . what will be the ratio in which they should share the profit at the end of the year ?
Options: a ) 20 : 9 , b ) 2 : 1 , c ) 3 : 2 , d ) 2 : 3 , e ) 5 : 3
a

Problem: find the ratio in which rice at rs . 7.20 a kg be mixed with rice at rs . 5.70 a kg to produce a mixture worth rs . 6.30 a kg ?
Options: a ) 1 : 3 , b ) 2 : 3 , c ) 3 : 4 , d ) 4 : 5 , e ) none of these
b

Problem: 7 machines at a certain factory operate at the same constant rate . if 6 of these machines , operating simultaneously , take 42 hours to fill a certain production order , how many fewer hours does it take all 7 machines , operating simultaneously , to fill the same production order ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
d