Question

2. Find the fraction which is equal to 1/2 when both its numerator and denominator are
increased by 2. It is equal to 3/4 when both are increased by 12.
a) 3/8
b) 5/8
c) 2/8
d) 2/3​

Answer 1

Step-by-step explanation:

I think their is mis-printing.... my answer is coming

3/7 not 3/8

sorry if it is incorrect

Answer 2

Step-by-step explanation:

$\bf\underline{\underline{\red{Given:-}}}$

• A fraction becomes ½ if both the numerator and denominator are increased by 2.

• If both are increased by 12 the fraction becomes ¾.

$\bf\underline{\underline{\blue{To\:Find:-}}}$

• The fraction.

$\bf\underline{\underline{\green{Solution:-}}}$

Let the numerator of the fraction be x

And the denominator be y

$\bf \pink{\underline{Case\: 1:-}}$

If numerator is increased by 2

The numerator = x + 2

If denominator is increased by 2

The denominator = y + 2

Given, the fraction becomes ½.

$\rm \implies \dfrac{x + 2}{y + 2} = \dfrac{1}{2}$

By cross multiplication:-

$\rm \implies {2(x + 2)} = {1(y + 2)}$

$\rm \implies {2x + 4} = {y + 2}$

$\rm \implies {2x - y} = { 2-4}$

$\rm \implies {2x - y} = { -2} ......(i)$

$\bf \orange{\underline{Case\: 2:-}}$

If numerator is increased by 12

The numerator = x + 12

If denominator is increased by 12

The denominator = y + 12

Given, the fraction becomes ¾.

$\rm \implies \dfrac{x + 12}{y + 12} = \dfrac{3}{4}$

By cross multiplication:-

$\rm \implies {4(x + 12)} = {3(y + 12)}$

$\rm \implies {4x + 48} = {3y + 36}$

$\rm \implies {4x - 3y} = {36 - 48}$

$\rm \implies {4x - 3y} = { -12} ......(ii)$

Multiplying equation (i) with 2

$\rm \implies {2(2x - y} = { -2)}$

$\rm \implies {4x - 2y} = { -4......(iii)}$

Subtracting equation (ii) from (iii)

$\rm \implies 4x - 2y -(4x - 3y) = - 4 - ( - 12)$

$\rm \implies 4x - 2y -4x + 3y = - 4 +12$

$\rm \implies y= 8$

Substituting y = 8 in equation (i)

$\rm \implies {2x - y} = { -2}$

$\rm \implies {2x - 8}= { -2}$

$\rm \implies {2x } = { -2+8}$

$\rm \implies {2x} = { 6}$

$\rm \implies {x} = { 3}$

The numerator = x = 3

The denominator = y = 8

$\underline{ \boxed{ \purple{\rm \therefore The \: fraction = \frac{3}{8} }}}$

$\rm Option \: (a) \: is \: correct$