In this task, you need to answer the given multiple-choice question on the general math. Classify your answers into 'a', 'b', 'c', 'd', and 'e'.

Problem: the ages of patrick and michael are in the ratio of 3 : 5 and that of michael and monica are in the ratio of 3 : 5 . if the sum of their ages is 147 , what is the difference between the ages of patrick and monica ? 
Options: a ) 48 , b ) 47 , c ) 46 , d ) 49 , e ) 52
a

Problem: each year for 4 years , a farmer increased the number of trees in a certain orchard by 1 / 4 of the number of trees in the orchard of the preceding year . if all of the trees thrived and there were 12500 trees in the orchard at the end of 4 year period , how many trees were in the orchard at the beginning of the 4 year period . 
Options: a ) 5113 , b ) 5117 , c ) 5120 , d ) 8119 , e ) 10115
c

Problem: if 12 : 8 : : x : 16 , then find the value of x 
Options: a ) 18 , b ) 24 , c ) 28 , d ) 16 , e ) 20

b