Question

The denominator of a rational number is greate thannumerator by 7.if the numerator is increased by 17 and the denominator is decreased by 6 the new number becomes 2. find the original number?
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Answer 1

Answer:

15/22

Step-by-step explanation:

Let the numerator be 'a' and denominator(greater by 7) is 'a + 7'.

Fraction is numer./denomi. = a/(a + 7)

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

New numerator = 'a + 17' , and

New denominator is 'a+7 - 6' = 'a+1'

As given,

=> (a + 17)/(a + 1) = 2

=> a + 17 = 2(a + 1)

=> a + 17 = 2a + 2

=> 17 - 2 = 2a - a

=> 15 = a

Original fraction is a/(a+7)=15/(15+7)

= 15/22

Answer 2

$\underline{ \large \purple{ \mathtt{\dag\:S \mathscr{olution࿐}}}}$

we need to find the original number .

${\green{ \mathscr{Let : - }}}$

• let the numerator be x

As it is given that denominator is greater then the numerator by 7,

• So, denominator is x + 7
• Fraction = x/(x + 7)

$\underline{ \large \purple{ \mathscr{\dag\:A \bf{ccourding} \: to \: \mathscr {Q} \bf{uestion} ....}}}$

if the numerator is increased by 17 and the denominator is decreased by 6 the new number becomes 2

So,

››➔ (x + 17)/(x + 7 - 6) = 2

››➔ (x + 17)/(x + 1) = 2

››➔ x + 17 = 2(x + 1)

››➔ x + 17 = 2x + 2

››➔ 17 - 2 = 2x - x

››➔ 15 = x

Numerator :

x = 15

Denominator :

x + 7 = 15 + 7

= 22

$\large\dag \large { \red{\underline{\bf{Hence }}}}$

• The original Fraction is 15/22

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