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

- Pair of Linear Equations in Two Variables Class 10 Ex 3.1
- Pair of Linear Equations in Two Variables Class 10 Ex 3.2
- Pair of Linear Equations in Two Variables Class 10 Ex 3.3
- Pair of Linear Equations in Two Variables Class 10 Ex 3.4
- Pair of Linear Equations in Two Variables Class 10 Ex 3.5
- Pair of Linear Equations in Two Variables Class 10 Ex 3.6
- Pair of Linear Equations in Two Variables Class 10 Ex 3.7

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 pairs of linear equations by the elimination method and the substitution method:

**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

**By Elimination method:**

(ii)

(ii)

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 for 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.

(ii)

**A.T.Q.**

1st Condition :

2nd Condition :

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

1st Condition :

2nd Condition :

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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