NCERT Solutions for Class 10 Mathematics Chapter 3 Pair of Linear Equations in Two Variables Ex 3.4 are part of NCERT Solutions for Class 10 Maths. Here we have given NCERT Solutions for Class 10 Mathematics Chapter 3 Pair of Linear Equations in Two Variables Ex 3.4.

Board |
CBSE |

Textbook |
NCERT |

Class |
Class 10 |

Subject |
Maths |

Chapter |
Chapter 3 |

Chapter Name |
Pair of Linear Equations in Two Variables |

Exercise |
Ex 3.4 |

Number of Questions Solved |
2 |

Category |
NCERT Solutions |

### NCERT Solutions for Class 10 Maths Chapter 3 Pair of Linear Equations in Two Variables Ex 3.4

**Question 1.**

Solve the following pair of linear equations by the elimination method and the substitution

(i) x + y = 5 and 2x – 3y = 4

(ii) 3x + 4y = 10 and 2x – 2y = 2

(iii) 3x – 5y – 4 = 0 and 9x = 2y + 7

(iv) x/2 + 2y/3 = -1 and x – y/3 = 3

**Solution:**

**(i)** By Elimination Method:

Fquations are x + y = 5

and 2x – 3y = 4

Multiply equation (i) by 2 and subtract equation (ii) from it, we have

**
(ii)** By Elimination method:

Equations are 3x + 4y = 10

and 2x – 2y = 2

Multiplying equation (ii) by 2 and adding to equation (i), we

**By Elimination Method:**

(iii)

(iii)

**(iv)** By Elimination Method:

**1st equation :**

**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 1 to the numerator and subtract 1 from the denominator, a fraction reduces to 1. It becomes – 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.

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

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

**Solution:**

**(i)** Let numerator be x and denominator be y.

Fraction = x/y

**A.T.Q.
(ii)** Let present age of Nuri be x years and Sonu’s present age bey years.

**A.T.Q.**

1st Condition :

2nd Condition :

Subtractomg equation (ii) from equetion (i), we get

Hence, present age of Nuri is 50 years and sonu’s present age is 20 years.

1st Condition :

2nd Condition :

Subtractomg equation (ii) from equetion (i), we get

Hence, present age of Nuri is 50 years and sonu’s present age is 20 years.

(iii) Let digit at unit place = x and digit at ten’s place = y.

Two digit number is lOy + x

**A.T.Q.**

**1st Condition :**

x + y = 9

**2nd Condition :**

9(10y + x) = 2(10k + y) ⇒ 90y + 9x = 20x + 2y

⇒ 88y – 11x = 0 ⇒ -11y + 88y = 0

⇒ -x + 8y = 0

Adding equestion (i) and (ii), we get

**(iv)** Let the number of notes of ₹ 50 = x and the number of notes of ₹ 100 = y

**A.T.Q**

**1st Condition :**

50x + 100y = 2000

⇒ x + 2y = 40

**2nd Condition :
**

(v) Let, fixed charge for first 3 days be ₹ x and additional charge per day after 3 days be y.

**A.T.Q.**

**1st Condition :** as per Saritha

x + 4y = 27

**2nd Condition :** as per Susy

Putting y = 3 in equation (i),

x + 4(3) = 27 ⇒ x + 12 = 27 ⇒ x = 15

Hence, fixed charge is ₹ 15 and charge for each extra day is ₹ 3.

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