Question

16. The numerator of a fraction is 7 less than the
denominator. If 3 is added to the numerator
and 2 is added to the denominator, the value
2
of the fraction becomes Find the original
3
fraction.
ş. Find the original​

Answer 1

Correct Question:-

$\text{The \: numerator \: of \: a \: fraction \: is \: 7 \: less \:}$$\text{less \:than \: the \:  denominator \: . If \: 3 \: is \: }$$\text{added \: to \: the \: numerator \: and \: 2 \: is \: added \: to }$$\text{\: the \: denominator \: , \: the \: value \: becomes }$$\text{\: 2/3 \: . \: Find \: the \: original \: fraction. \: }$

Solution:-

Let the numerator be x and

the denominator be y

Given,

The numerator of a fraction is 7 less than the  denominator.

x + 7 = y  ..... 1

If 3 is added to the numerator  and 2 is added to the denominator, the value becomes 2/3.

️ ➭ ( x + 3 ) / ( y + 2 ) = 2/3

️ ➭ $\text{ 3 \: (x \: + \: 3) \: = \: 2 \: ( \: y \: + \: 2 \: )}$

️ ➭ $\text{ 3x \: + \: 9 \: = \: 2y \: + \: 4 \:}$

️ ➭ $\text{ 3x \: - \: 2y \: = \: -9 \: + \: 4 \:}$

️ ➭ $\text{ 3x \: - \: 2( x + 7 ) = \: -9 \: + \: 4 \:}$

️ ➭ $\text{ 3x \: - \: 2x \: - \: 14 =\: -5 \:}$

️ ➭ $\text{ x \: = \: 14 \: - \: 5 \:}$

️ ➭ $\tt\boxed { \: x \: = \: 9 \: }$

Then,

The denominator is

️ ➭ $\text{ y \: = \: x \: + \: 7 \:}$

️ ➭ $\text{ y \: = \: 9 \: + \: 7 \:}$

️ ➭ $\tt \boxed { \: y \: = \: 16 \: }$

The fraction is  $\dfrac{9}{16}$

Answer 2

$\underline{ \underline{ \sf \maltese\:{Correct ~ question:-}}}$

The numerator of a fraction is 7 less than the denominator. If 3 is added to the numerator and 2 is added to the denominator, the value of the fraction becomes 2/3. Find the original fraction.

$\underline{ \underline{ \sf \maltese\:{Given:-}}}$

• Numerator of the fraction is 7 less than the denominator.
• The value of the fraction becomes 2/3 when 3 is added to the numerator and 2 is added to the denominator.

$\underline{ \underline{ \sf \maltese \:{To \: find:-}}}$

• The original fraction.

$\underline{ \underline{ \sf \maltese \:{Solution:-}}}$

Let:-

• The numerator = x
• The denominator = y

Since,

Numerator of the fraction is 7 less than the denominator.

∴ y - 7 = x

⇒ y = x + 7

Since,

The value of the fraction becomes 2/3 when 3 is added to the numerator and 2 is added to the denominator.

∴ $\sf\dfrac{x + 3}{y + 2} = \dfrac{2}{3}$

⇒ 3(x + 3) = 2(y + 2)

⇒ 3x + 9 = 2y + 4

⇒ 3x + 9 = 2(x + 7) + 4

⇒ 3x + 9 = 2x + 14 + 4

⇒ 3x - 2x = 18 - 9

⇒ x = 9

∴ the numerator = x = 9

∴ the denominator = y = x + 7 = 9 + 7 = 16

∴ the original fraction = $\sf\dfrac{9}{16}$