Question

the numerator of a fraction is 6 less than the denominator.If the numerator is reduced by 2 and the denominator is increased by 3 the fraction becomes 3/14.Find the original fraction

Answer 1

the answer is 11. the original fraction is 3/14

Answer 2

Required fraction = 5/11

Given:

The numerator of a fraction is 6 less than the denominator

When the numerator is reduced by 2 and the denominator is increased by 3 the fraction becomes 3/14

To find:

Find the required fraction

Solution:

Let x/y be the fraction

Given that the numerator of a fraction is 6 less than the denominator

⇒ x = y-6 ---(1)

Then x/y = (y-6)/y

The numerator is reduced by 2

⇒ y-6  ⇒ y-6-2 = y - 8

The denominator is increased by 3

⇒ y  ⇒ y+3

After all changes the final fraction = y-8/y+3

From given data, $\frac{y-8}{y+3} =\frac{3}{14}$  

⇒  $14(y-8) = 3(y+3)$  

⇒  $14y-112 = 3y+9$

⇒ 11y = 121

⇒ y = 11  

From (1) x = 11 -6 = 5

Therefore, Required fraction = 5/11

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