Question
Wed July 18, 2012 By:
 

if 2 is added to each of two given numbers, their ratio becomes 1:2. however, if 4 is subtracted from each of the given numbers, the ratio becomes 5:11. find the numbers.

Expert Reply
Thu July 19, 2012
Answer : Given : if 2 is added to each of two given numbers, their ratio becomes 1:2. however, if 4 is subtracted from each of the given numbers, the ratio becomes 5:11.
To find : the two numbers.
 
Let x and y be the two numbers.
 
according to the question,
If 2 is added to each of two given numbers, their ratio becomes 1:2. 
=> ( (x + 2) / ( y+2) ) = 1/2 
=> 2x - y = - 2
=> y = 2x + 2....................................................(1)
 
if 4 is subtracted from each of the given numbers, the ratio becomes 5:11.
=> ( ( x - 4 ) / ( y-4 ) ) = 5 /11
=> 11x - 5y= 24.............................................(2)
 
substituting the value of y from eq (1) in eq(2) , we get
=> 11 x - 5( 2x+2) = 24
=> 11x - 10x  = 34
=> x= 34
 
y = 2x + 2
=> y = 2(34) +2 = 68 + 2
=> y = 70
 
Answer : the two required numbers are x = 34 and y = 70  
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