July 2010 Q3

Question

The product of the ages of a boy and his father is 900. In 2 years time the product of their ages will be 1040. How old is each today?

Answer 1

FB = 900    

(F+2)(B+2) = 1040

 

FB +2F + 2B + 4 = 1040

 

900 + 2F + 2B + 4 = 1040

 

2F + 2B = 1040 - 4 - 900 

 

2F + 2B = 136

 

2(F + B) = 136

 

F + B = 68

 

F = 68 - B

 

FB = 900

 

(68 - B)B = 900

 

0 = B^2 -68B + 900

 

0 = (B-50)(B-18)

 

B = 50 OR B = 18

 

Boy is 18 and 900/18 = 50 is the father