Question

The denominator of a rational number is greater than its numerator by 7. If the

numerator is increased by 17 and denominator decreased by 6, the new number

becomes 2. Find the original number?​

Answer 1

Answer:

15/22

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Answer 2

Given :-

• The denominator of a rational number is greater than its numerator by 7.

• If the numerator is increased by 17 and denominator decreased by 6,the new number becomes 2.

To find :-

• The original number

Solution :-

Let the numerator of rational number be x

and denominator of rational number be x + 7

⪼ Numerator is increased by 17,

• (x + 17)

⪼ Denominator is decreased by 6,

• (x + 7) - 6

According to the Question,

$\rm\:\dfrac{x+17}{(x+7)-6}=2$

$\rm\longrightarrow\:\dfrac{x+17}{x-1}=2$

By cross multiplication,

$\rm\longrightarrow\:x+17=2(x+1)$

$\rm\longrightarrow\:x+17=2x+2$

$\rm\longrightarrow\:x-2x=2-17$

$\rm\longrightarrow\:\cancel{-}x=\cancel{-}15$

$\rm\longrightarrow\:x=15$

Therefore,the numerator will be 15,

And Denominator = x + 7

Denominator = 15 + 7

Denominator = 22

Hence,the original number will be15/22.