1
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Question

# When 6 is added to the numerator of a fraction, the numerator becomes twice the denominator. In another fraction, 10 times the denominator exceeds 5 times the numerator by 30. The number of solutions for the given equations is

A

0

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B

1

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C

2

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D

Infinitely many solutions

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Solution

## The correct option is D Infinitely many solutions Case1 : Let the fraction be xy Given that, x+6=2y ⇒x−2y+6=0 Case 2 : Let the fraction be xy Given that, 10y−5x=30 ⇒5x–10y+30=0. From the equations x−2y+6=0 and 5x–10y+30=0. a1a2=15,b1b2=−2−10=15,c1c2=630=15 ⇒a1a2=b1b2=c1c2 ∴ The pair of equations has infinite number of solutions.

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