Question

Numerator of a fraction is 5 more than its denominator. If 4 is added to

numerator and denominator, the fraction obtained is 6

5

. Find the fraction.​

Answer 1

☯GIVEN :

• Numerator of a fraction is 5 more than its denominator.

• If 4 is added to numerator and denominator , the fraction obtained is $\bf{\dfrac{6}{5}}$

☯TO FIND :

• Required fraction.

➲SOLUTION :

Let denominator be x

Then , numerator = x+5

• After adding 4 to numerator and denominator , the fraction obtained is $\bf{\dfrac{6}{5}}$.

$\implies{ \sf{ \dfrac{(x + 5) + 4}{x + 4} = \dfrac{6}{5} }}$

$\implies{ \sf{ \dfrac{x + 5 + 4}{x + 4} = \dfrac{6}{5} }}$

$\implies{ \sf{ \dfrac{x + 9}{x + 4} = \dfrac{6}{5} }}$

• By cross multiplication :

$\implies{ \sf{5(x + 9) = 6(x + 4)}}$

$\implies{ \sf{5x + 45= 6x + 24}}$

$\implies{ \sf{45 - 24= 6x - 5x }}$

$\implies{ \sf{21= x }}$

$\implies{ \underline{ \bf{x = 21}}}$

• ★Denominator = 21

• ★ Numerator = 21+5 = 26

$\huge {\pink{\therefore}}$The original fraction is $\bf{\dfrac{26}{21}}$.