Question 2. Form the Pair of Linear Equations in the Following P Exercise 3.4 Chapter 3 Pair of Linear Equations in

Question 2. 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 1tothe numerator and subtract 1fromthe denominator, a fractionreduces to 1. It becomes1/2 if we only add 1 to the denominator.What is the  raction?
(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.
(iv) Meena went to a bank to withdraw Rs 2000. She asked the cashier to give her Rs 50 and Rs 100 notes only. Meena got 25 notes in all. Find how many notes of Rs 50 and Rs 100 she received.
A lending library has a fixed charge for the first three days and an additional charge for each day thereafter. Saritha paid Rs 27 for a book kept for seven days, while Susy paid Rs 21 for the book she kept for five days. Find the fixed charge and the charge for each extra day.
Answers:-
(i) If we add 1tothe numerator and subtract 1fromthe denominator, a fraction reduces to 1. It becomes1/2 if we only add 1 to the denominator. What is the fraction?
Let numerator = x
And denominator = y
Fraction  = x/y
If we add 1tothe numerator and subtract 1fromthe denominator, a fractionreduces to 1
 
Croos multiply we get
x + 1  = y – 1
x- y =  -2         ……..(1)
It becomes1/2 if we only add 1 to the denominator.

Croos multiply we get
2x   = y + 1
2x- y =  1        ……..(2)
x- y =  -2         ……..(1)
Subtracting equation (1) from equation (2) we get

x  = 3

Substituting this value in equation (1) we get
3– y = - 2
- y =  - 5
y = 5
Hence our fraction is 3/5
(ii) Fiveyears 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?

Let the present age of Nuri  = x year
And present age of Sonu = y year
Five years ago
Age of Nuri = x – 5 years
Age of Sony = y – 5 years
Nuri was thrice as old as Sonu
x- 5  =  3(y – 5)
x – 5  =  35 – 15
x – 3y  =  -15  + 5
x – 3 y  = - 10                        ………..(1)
Ten years later,
Age of Nuri  = x + 10
Age of Sonu = y + 10
Nuri will be twice as old as Sonu.
x+ 10 = 2(y+10)
x + 10  = 2y + 20
x – 2y  = 10                           ………..(2)
x – 3 y  = - 10                        ………..(1)
Subtracting equation (1) from equation (2)  we get
y  = 20
Plug this value in equation first we get
x  - 3* 20 = -10
x = 60 – 10
x  = 50

Hence age  of Nuri = 50 years and age of Sonu  = 20 years

(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.
Let unit digit  = x
Tens digit  = y
Number will 10 times the tens digit + unit times the unit digit
Hence number will 10 y + x

Sum of digits are 9
So that
x + y  = 9        ………….(1)
nine times this number is twice the number obtained by reversing the order of the digits

9 (10 y + x )  =  2 (10 x + y )
90 y + 9 x  = 20 x + 2y
88 y – 11 x  = 0
Divide by 11 we get
8 y  - x  = 0     …………..(2)
x + y  = 9        ………….(1)

Adding both equations we get
9 y = 9
y = 9/9 = 1
Plug this value in equation first we get
x+ y = 9
x + 1 = 9
x = 8
So our original number is 10 y  + x    = 10*1 + 8  = 18
(iv)Meena went to a bank to withdraw Rs 2000. She asked the cashier to give her Rs 50 and Rs 100 notes only. Meena got 25 notes in all. Find how many notes of Rs 50 and Rs 100 she received.

Let the number of Rs 50 notes  = x
The number of Rs 100 notes  =y
According to the given information
Meena went to a bank to withdraw Rs 2000
So cost of 50 rupee notes  = 50x
And cost of 100 ruppe notes  = 100 y
Total cost is Rs 2000
So that
50 x + 100 y  = 2000
Divide by 50 we get
x + 2 y = 40               ………(1)

Meena got 25 notes in all so that
x +  y  = 25                ………(2)
x + 2 y = 40               ………(1)

Subtracting equation (1) from (2 we get
-y = - 15
y = 15
Plug this value in equation first we get
x + 2*15 =  40
x +  30  = 40
x = 10
Hence 50 rupee notes are 10 and 100 Rupee notes are 15

(v)Alending library has a fixedcharge for the first three days and an additional charge for each day thereafter. Saritha paid Rs 27 for a book kept for seven days, while Susy paid Rs 21 for the book she kept for five days. Find the fixed charge and the charge for each extra day.
Let fixed change =Rs x
And charge for extra day  = Rs  y
Saritha paid Rs 27 for a book kept for seven days
So first three days she paid  Rs x   and for remaining 4 days she will pay 4y
So total paying
x + 4 y = 27               …….. (1)
Similarly
For while Susy paid Rs 21 for the book she kept for five days
x + 2y  = 21               ……..(2)
x + 4 y = 27               …….. (1)
Subtracting equation (1) from equation (2), we get
-2 y  = - 6
y = 3
Plug this value in equation (1) we get
x + 4 y = 27               …….. (1)
x + 4 (3)  = 27
x = 27 – 12
x = 15
Hence fixed cost is Rs 15 And cost for extra each day is Rs 3