SSC (English Medium) Class 8Maharashtra State Board
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# The Denominator of a Fraction is Greater than Its Numerator by 12. If the Numerator is Decreased by 2 and the Denominator is Increased by 7, - SSC (English Medium) Class 8 - Mathematics

ConceptWord Problems of Equation in One Variable

#### Question

The denominator of a fraction is greater than its numerator by 12. If the numerator is decreased by 2 and the denominator is increased by 7, the new fraction is equivalent with 1/2. Find the fraction.

#### Solution

Let the numerator of the fraction be x.

∴ Denominator = x + 12

∴ The fraction = "x"/("x" + 12)

If the numerator is decreased by 2 and the denominator is increased by 7, the new fraction obtained is 1/2.
From the given information,

("x" - 2)/("x" + 12 + 7) = 1/2

⇒ 2 (x - 2) = 1 ( x + 12 +7)

⇒  2x - 4 = x + 19

⇒  2x - x = 19 + 4

⇒  x = 23

∴ Numerator of the fraction is 23.
∴ Denominator of the fraction is 23 + 12 = 35.

Hence, the fraction is 23/35.

Is there an error in this question or solution?

#### APPEARS IN

Balbharati Solution for Balbharati Class 8 Mathematics (2019 to Current)
Chapter 12: Equations in one variable
Practice Set 12.2 | Q: 2 | Page no. 79
Solution The Denominator of a Fraction is Greater than Its Numerator by 12. If the Numerator is Decreased by 2 and the Denominator is Increased by 7, Concept: Word Problems of Equation in One Variable.
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