Problems on Compound Proportion

compound proportions contain three or more different kinds of quantities involving two or more simple proportions.

Rule to solve compound proportion problems:-
i) select all the quantities given in the problem such as man, work, hour and day, etc.

ii) put all the quantities in one line keeping the required quantity to the right-hand side.

iiI)  without considering the quantities in (i) write I, II, III, and IV. 

iv) below III put the last quantity in which the answer is wanted. below IV put x. put the sign of ratio : between III and IV and a sign of proportion:: between II and III.

v) now find out by careful inspection whether the quantities to be found out is greater or less than the third term.

if greater put the lesser of the two as the first term. if less put the greater of the two as the first term and the other as the second term.

divide the product of all the terms below II and III by the product of all the two as below I.

Example 1:  if 5 men can do a piece of work in 20 days, in how many days will 10 men and 5 boys do the same work if one men does as much work  as 2 boys.
Solution : 
according to the above rule we write all in a line (men, boys, and days)
MEN         BOYS          DAYS
5                   0                 20
10                  5                ?
here given a men work much of 2 boys so 1 men = 2boys.
5men +0boys = 20 days
10 men  + 5 boys = ?
5 men  = 20 days
1 men = 20 * 5 = 100 days
here days and men are inversey proportional.
10 men  + 5/2 men ( as 1 men = 2boys) = 100 / (25/2) = 200/25 = 8 Days Answer.