Question

If numerator of a fraction is increased by 2 and the denominator by 1 it becomes 5/8 and if numerator and denominator of a fraction are each increased by 1 the fraction becomes 1/2.Find the fraction.​

Answer 1

Answer:

3/7

Step-by-step explanation:

⊛Given:-

If numerator of a fraction is increased by 2 and the denominator by 1 it becomes 5/8 and if numerator and denominator of a fraction are each increased by 1 the fraction becomes 1/2.

⊛To Find:-

The Fraction

⊛Solution:-

$\maltese \: \color{aqua} \rm \: Let \: the \: numerator \: and \: denominator \\ \rm \: be \: x \: and \: y \: respectively$

When Numerator is increased by 2

Numberator = x+2

When denominator is increased by 1

Denominator = y+1

$\rm \: Now \: fraction = \frac{x + 2}{x + 1}$

So,

$\rm \: \frac{x + 2}{y + 1} = \frac{5}{8} \\ \sf \: by \: cross - multiplying \\ \rm \: 8(x + 2) = 5(y + 1) \\ \rm\rightarrowtail \: 8x + 16 = 5y + 5 \\ \rm\rightarrowtail \:8x - 5y = - 11 - - - (i)$

When Numerator is increased by 1

Numerator=x+1

When denominator is increased by 1

Denominator=y+1

So,

$\rm \: \frac{x + 1}{y + 1} = \frac{1}{2} \\ \rm\rightarrowtail \:2(x + 1) = 1(y + 1) \\ \rm\rightarrowtail \:2x + 2 = y + 1 \\\rm\rightarrowtail \: 2x - y = - 1 - - - (ii)$

Now, Multiply (ii) by 5 and then subtracting it from (i)

$\rm \: 5(2x - y = - 1) \\ \rm\rightarrowtail \:10x - 5y = - 5 \\ \\ \rm 8x - 5y = - 11 \\ \rm \: 10x - 5y = - 5 \\ - \: \: \: \: \: \: \: \: + \: \: \: \: \: \: \: \: \: \: \: + \: \: \: \\ - - - - - - - - \\ \rm \: - 2x = - 6 \\ \rm 2x = 6 \\ \rm x = 3$

So, Numerator = 3

Putting x in eq. (ii)

2(3)-y=-1

6-y=-1

-y=-1-6

-y=-7

y=7

So, Fraction=Numerator/Denominator=3/7