Question

A fraction's value is 4/5. When its numerator
is increased by 9, the new fraction equals
the reciprocal of the value of the original
fraction. Find the original fraction.​

Answer 1

1+1 =2 4-76= _ 74 shivanes is the time to start my day

Answer 2

Let :

• Numerator = x
• Denominator = y

Given :

$\sf \bullet \: \: \dfrac{x}{y} = \dfrac{4}{5}$

$\sf \bullet \: \: \dfrac{x + 3}{y} = \dfrac{y}{x} = \dfrac{5}{4}$

To find :

$\sf \: \dfrac{x}{y}$

Solution :

$\sf \: \: x = \dfrac{4y}{5} \: \: .......equation1$

$\sf \implies \: \: \: \dfrac{x + 9}{y} = \dfrac{5}{4} \\ \\ \sf \implies \: \: x + 9= \dfrac{5}{4} y \\ \\ \sf \: putting \: value \: of \: x \: from \: equation \: 1 \: we \: get \: \\ \sf \implies \: ( \dfrac{4y}{5} ) + 9= \dfrac{5y}{4} \\ \\ \sf \implies \: 0.8y + 9 = 1.25y \\ \sf \implies \: 1.25y - 0.8y = 9 \\ \sf \implies \: 0.45y = 9 \\ \sf \implies \: y \: = \: \dfrac{9}{0.45} = 20$

Putting value of y in equation 1, we get;

x = 4×20/5 = 4×4

x = 16

ANSWER :

Numerator (x) = 16

Denominator (y) = 20

$\sf \bold{Fraction = \dfrac{16}{20} }$