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

(i) If we add 1 to the numerator and subtract 1 from the denominator, a fraction reducesto 1. It becomes1/2 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 asold 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 istwice the number obtained by reversing the order of the digits. Find the number.

(iv) Meena went to a bank to withdraw Rs 2000. She asked the cashier to give herRs 50 and Rs 100 notes only. Meena got 25 notes in all. Find how many notes ofRs 50 and Rs 100 she received.

(v) A lending library has a fixed charge for the first three days and an additional chargefor each day thereafter. Saritha paid Rs 27 for a book kept for seven days, whileSusy paid Rs 21 for the book she kept for five days. Find the fixed charge and thecharge for each extra day.

Solution: y = 20

Putting value of y in equation  (i) we get,

x - 60 = -10

x = 50

Hence,

Present age of Nuri = %0 years

Present age of Sonu = 20 yrears v. Let the fixed charge for first three days = Rs. x

Let each day charge there after  = Rs. y

According to the question,

x + 4y = 27.................(i)

x + 2y = 21 ................(ii)

Subtracting equation (ii) from equation (i) we get,

2y = 6

= y = 6/2 = 3

Putting value of y in equation (i). we get,

x + 12 = 27

= x = 27 - 12 = 15

Hence,

Fixed charge  = Rs. 15

Charge per day = Rs. 3