Q. 415.0( 3 Votes )

The product of Tanvy's age (in years) 5 years ago and her age 8 years later is 30. Find her present age.

Answer :

Let the present age of Tanvy be x years

Tanvy’s age five years ago = (x – 5) years


Tanvy’s age eight years from now = (x + 8) years


(x – 5)(x + 8) = 30


x2 + 3x – 40 = 30


x2 + 3x – 70 = 0


Using the splitting middle term – the middle term of the general equation is divided in two such values that:


Product = a.c


For the given equation a = 1 b = 3 c = – 70


= 1. – 70 = – 70


And either of their sum or difference = b


= 3


Thus the two terms are 10 and – 7


Difference = 10 – 7 = 3


Product = 10. – 7 = – 70


x2 + 10x – 7x – 70 = 0


x (x + 10) – 7(x + 10) = 0


(x + 10) (x – 7) = 0


x = – 10 or x = 7 (age cannot be negative)


x = 7


The present age of Tanvy is 7 years


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