A fraction is such that if the numerator is multiplied by 3 and the denominator is reduced by 3, we get 18/11, but if the numerator is increased by 8 and the denominator is doubled, we get 2/5. Then the fraction is

Correct Answer is : 122512/252512

Correct Answer is : 122512/252512

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Question : 12 of 39

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3,

\frac{18}{11}

\frac{2}{5}.

Then the fraction is

Solution:

Concept:

Form equations from the given conditions and solve for the numerator and denominator.

Explanation:

Let the fraction be

\frac{x}{y}

From first condition:

\frac{3x}{y-3} = \frac{18}{11}

Cross-multiplying:

33x = 18(y-3)

\implies

33x = 18y - 54

\implies

11x = 6y - 18

Thus,

6y = 11x + 18

and

y = \frac{11x + 18}{6}

From second condition:

\frac{x+8}{2y} = \frac{2}{5}

Cross-multiplying:

5(x+8) = 4y

\implies

5x + 40 = 4y

\implies

y = \frac{5x + 40}{4}

Equate the two expressions for

y

\frac{5x+40}{4} = \frac{11x+18}{6}

Cross-multiply:

6(5x+40) = 4(11x+18)

\implies

30x + 240 = 44x + 72

\implies

240 - 72 = 44x - 30x

\implies

168 = 14x

\implies

x = 12

Then

y = \frac{5(12)+40}{4} = \frac{60+40}{4} = \frac{100}{4} = 25

Thus the fraction is

\frac{12}{25}

Answer:

\frac{12}{25}

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