Question

the denominator of a rational number is greater than is number by 7. if the
numerator is increased by 17 and the denominator decrease by 6, the new
number becomes 2. Find the original number.
sn
and 55, find the numbers.
5.
fraction, twice the numerator is ? more than​

Answer 1

Answer:

Step-by-step explanation:

Let the rational numbers be

According to the question

y = x + 7x = y - 7....(1)

And $\frac{x+17}{y-6}$ = 2

Putting (1), we get,

$\frac{y-7+17}{y-6}$=2

By cross multiplication

⇒ y - 7 + 17 = 2(y - 6)

⇒ y + 10 = 2y - 12

⇒ 2y - y = 10 + 12

⇒ y = 22

⇒ x = y - 7 = 22 - 7 = 15

So the number is $\frac{15}{22}$

Answer 2

Appropriate Question:

• The denominator of a rational number is greater than its numerator by 7. If the numerator is increased by 17 and denominator is decreased by 6, the new number formed becomes 2. Find the original number.

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

❒ Let the numerator be x. And, the Denominator be (x + 7).

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⠀

$\qquad\quad\boxed{\bf{\mid{\overline{\underline{\bigstar\: According\: to \; the\; Question \: :}}}}\mid}$

⠀

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

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Therefore,

• Numerator, x = (x + 17)

Also,

• Denominator, (x + 7 - 6) = (x + 1)

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Now,

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$:\implies\sf \dfrac{\Big(x + 17 \Big) }{\Big(x + 1 \Big)} = 2 \\\\\\:\implies\sf \Big(x + 17 \Big) = 2 \Big(x + 1 \Big) \\\\\\:\implies\sf x + 17 = 2x + 2\\\\\\:\implies\sf 2x - x = 17 - 2\\\\\\:\implies{\underline{\boxed{\frak{\pink{x = 15}}}}}\;\bigstar$

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Hence,

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• Numerator, x = 15

• And, Denominator, (x + 7) = 15 + 17 = 22

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$\therefore{\underline{\sf{Hence, \: the\; original\; number\;is \; \bf{\dfrac{15}{22}}.}}}$