Question
Fri March 06, 2015 By: Ayushi Jain

Two years ago, a man's age was three times the square of his son's age.In three years time, his age will be four times his son's age.Find their present age.

Expert Reply
Prasenjit Paul
Sat March 07, 2015
L e t space t h e space p r e s e n t space a g e space o f space t h e space m a n space a n d space h i s space s o n space b e apostrophe m apostrophe space y e a r s space a n d space apostrophe s apostrophe space y e a r s space r e s p e c t i v e l y. T w o space y e a r s space a g o comma M a n apostrophe s space a g e space equals space left parenthesis m minus 2 right parenthesis S o n apostrophe s space a g e space equals space left parenthesis s minus 2 right parenthesis left parenthesis m minus 2 right parenthesis equals 3 left parenthesis s minus 2 right parenthesis squared m minus 2 equals 3 s squared minus 12 s plus 12 m equals 3 s squared minus 12 s plus 14...... left parenthesis i right parenthesis  T h r e e space y e a r s space l a t e r comma M a n apostrophe s space a g e space equals space left parenthesis m plus 3 right parenthesis S o n apostrophe s space a g e space equals left parenthesis s plus 3 right parenthesis m plus 3 equals 4 left parenthesis s plus 3 right parenthesis m minus 4 s equals 9......... left parenthesis i i right parenthesis  E q u a t i n g space left parenthesis i right parenthesis space a n d space left parenthesis i i right parenthesis comma 4 s plus 9 equals 3 s squared minus 12 s plus 14 3 s squared minus 16 s plus 5 equals 0 3 s squared minus 15 s minus s plus 5 equals 0 3 s left parenthesis s minus 5 right parenthesis minus 1 left parenthesis s minus 5 right parenthesis equals 0 left parenthesis 3 s minus 1 right parenthesis left parenthesis s minus 5 right parenthesis equals 0 s equals 5 comma space s equals 1 third left square bracket N o t space p o s s i b l e right square bracket therefore s equals 5 space y e a r s m equals 29 P r e s e n t space a g e space o f space m a n space equals 29 space y e a r s P r e s e n t space a g e space o f space s o n space equals space 5 space y e a r s
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