NCERT Class X Chapter 3: Pair of Linear Equations In Two Variables Exercise 3.2 Question 3(v)

NCERT Class X Chapter 3: Pair of Linear Equations In Two Variables Exercise 3.2 Question 3(v)

Question:

Form the pair of linear equations for the following problems and find their solution by substitution method.

A fraction becomes 911 if 2 is added to both the numerator and the denominator. If, 3 is added to both the numerator and the denominator it becomes 56. Find the fraction

Given:

A fraction becomes 911 if 2 is added to both the numerator and the denominator. If 3 is added to both the numerator and the denominator, it becomes 56.

To Find:

The fraction.

Formula:

Let the fraction be xy. Then, x+2y+2 = 911 and x+3y+3 = 56

Solution:

11(x+2) = 9(y+2) ⇒ 11x + 22 = 9y + 18 ⇒ 11x - 9y = -4 ...(1)

6(x+3) = 5(y+3) ⇒ 6x + 18 = 5y + 15 ⇒ 6x - 5y = -3 ...(2)

From (2), 6x = 5y -3 ⇒ x = 5y-36

Substitute in (1): 11(5y-36) - 9y = -4 ⇒ 55y - 33 - 54y = -24 ⇒ y = 9

Substitute y = 9 in x = 5y-36 ⇒ x = 5(9)-36 = 426 = 7

Result:

Therefore, the fraction is 79.

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