Form the pair of linear equations in the following problems, and find their solutions (if they exist) by the elimination method :

Question

(i) If we add 1 to the numerator and subtract 1 from the denominator, a fraction reduces to 1. It becomes 1/2 if we only add 1 to the denominator. What is the fraction?
(ii) Five years ago, Nuri was thrice as old as Sonu. Ten years later, Nuri will be twice as old as Sonu. How old are Nuri and Sonu?
(iii) The sum of the digits of a two-digit number is 9. Also, nine times this number is twice the number obtained by reversing the order of the digits. Find the number.

Answer 1

(i) Let the fraction be x/y

According to the given conditions

(ii) Let the present age of Nuri be x (in years) and Present age of Sonu be y (in years)

According to the given conditions,

Hence, Present age of Nuri is 50 years and present age of Sonu is 20 years

(iii) Let x be the digit at unit's place and y be the digit at ten's place.

According to the given condition