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: gold is 19 times as heavy as water and copper is 9 times as heavy as water . in what ratio should these be mixed to get an alloy 15 times as heavy as water ? 
Options: a ) 3 : 2 , b ) 3 : 8 , c ) 5 : 7 , d ) 3 : 7 , e ) 3 : 6
a

Problem: there were 35 students in a hostel . due to the admission of 7 new students , he expenses of the mess were increased by rs . 42 per day while the average expenditure per head diminished by rs 1 . what was the original expenditure of the mess ? 
Options: a ) 125 , b ) 321 , c ) 561 , d ) 852 , e ) 420
e

Problem: in a classroom , the average age of boys ( b ) is g and the average age of girls ( g ) is b . the average age of all is b + g . at the time of calculation , the class teacher , who is 42 years old was also present in the class . can you find the value of b + g ? 
Options: a ) 8 , b ) 3 , c ) 7 , d ) 9 , e ) 10

a