Five years ago Bina ‘s age was the square of Seema ‘s age . In fifteen years , Bina ‘s Age would be 1.5 times Seema’s age . Find present ages Take Seema’s age five Years ago to be ‘ x ‘ .
Answers
Given :
Age of Seema five years ago = x .
To find :
Present age of Seema and Bina .
Solution :
Let Bina's age fives year ago be y .
Bina's age five years ago , y = x * x .....(i)
After fifteen years from now ,
y + 20 = ( 3 / 2 ) * ( x + 20 )
using equation (i) ,
x * x + 20 = ( 3 / 2 ) * ( x + 20 )
=> 2 ( x * x ) - 3 x - 20 = 0
=> ( 2x + 5 )( x - 4 ) = 0
=> x = 4 {age can not be negative}
Present age of Bina = x * x + 5 = 21
Present age of Seema = x + 5 = 9
The present age of Bina is 21 and the present age of Seema is 9 .
Given : Five years ago Bina ‘s age was the square of Seema ‘s age . In fifteen years , Bina ‘s Age would be 1.5 times Seema’s age .
To find : present ages
Solution:
Seema’s age five Years ago = x years
Seema present age = x + 5 years
Seema age after 15 years = x + 5 + 15 = x + 20 Years
Five years ago Bina ‘s age was the square of Seema ‘s age
Five years ago Bina ‘s age = x²
Bina present age = x² + 5 years
Bina age after 15 years = x² + 5 + 15 = x² + 20 Years
In fifteen years , Bina ‘s Age would be 1.5 times Seema’s age
=> x² + 20 = 1.5(x + 20)
=> x² - 1.5x - 10 = 0
=> x² - 4x + 2.5x - 10 = 0
=> x(x - 4) + 2.5(x - 4) = 0
=> (x + 2.5)(x - 4) = 0
=> x = 4
Seema present age = 4 + 5 = 9 years
Bina present age = 4² + 5 = 21 years
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