a fraction becomes 1/3 when 2 is subtracted from the numerator and it becomes 1/4

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A fraction becomes 13 when 2 is subtracted from the numerator and it becomes 12 when 1 is subtracted from the denominator. Find the fraction.

Click here👆to get an answer to your question ✍️ A fraction becomes 13 when 2 is subtracted from the numerator and it becomes 12 when 1 is subtracted from the denominator. Find the fraction.

A fraction becomes

Question 3 1

when 2 is subtracted from the numerator and it becomes

2 1

when 1 is subtracted from the denominator. Find the fraction.

Let the fraction be

Easy Open in App Solution Verified by Toppr y x

From the given conditions

y x−2 = 3 1 ⟹y=3x−6⋯(1) y−1 x = 2 1 ⟹y=2x+1⋯(2) From (1)&(2)

2x+1=3x−6⟹x=7⟹y=3(7)−6=15

So the fraction is 15 7

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A Fraction Becomes 1 3 When 2 is Subtracted from the Numerator and It Becomes 1 2 When 1 is Subtracted from the Denominator. Find the Fraction.

Advertisement Remove all ads Sum A fraction becomes 13

when 2 is subtracted from the numerator and it becomes

when 1 is subtracted from the denominator. Find the fraction.

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SOLUTION

Let's assume the fraction be

x y xy

1st condition:

x y x-2y=13 ⇒ xy 3x -6=y ⇒ xy 3x-y=6 ...(1)

2nd condition:

x y xy-1=12 ⇒ xy 2x-y-1 ⇒ xy 2x-y=-1

Using elimination method:

Multiplying (2) by -1 and then adding (1) and (2)

⇒ xy 3x-y=6 ⇒ xy -2x+y=1 ⇒ x x=7 Now, from (1) ⇒ xy 3x-y=6 ⇒ y 3(7)-y=6 ⇒ y 21-y=6 ⇒ y y=15

Hence, the required fraction is

715

Concept: Algebraic Methods of Solving a Pair of Linear Equations - Elimination Method

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A fraction becomes 1 / 3 when 2 is subtracted from the numerator and it becomes 1 / 2 when 1 is subtracted from the denominator. Find the fraction.

Byju's Answer Standard X Mathematics

Elimination Method of Finding Solution of a Pair of Linear Equations

A fraction be... Question

A fraction becomes 1/3 when 2 is subtracted from the numerator and it becomes 1/2 when 1 is subtracted from the denominator. Find the fraction.

Open in App Solution

Let the numerator of the fraction be x and the denominator be y.

According to the question,

x-2y=13...(i) andxy-1=12...(ii)

Solvingequationi,weget

3x-2=y ⇒3x-6=y...iii

Substitutingthevalueofyinequationii,weget

x3x-6-1=12 ⇒2x=3x-6-1 ⇒2x=3x-7 ⇒2x-3x=-7 ⇒-x=-7 ⇒x=7...(iv)

From(iii)and(iv),weget

x=7andy=15

Hence,thefractionis715.

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