Question

The numerator of a fraction is 6 less than the denominator. If 3 is added to the numerator, the fraction becomes equal to 2/3. Find the original fraction.

Answer 1

Let the denominator be x
numerator =x-6
Fraction=x-6/x

According to question
x-6+3/x=2/3
x-3/x=2/3
3 (x-3)=2x
3x-9=2x
x=9

Numerator=9-6=3
Denominator=9
Fraction=3/9=1/3

Answer 2

${\fbox{\huge\sf{\pink{An}\purple{sW}\green{eR}}}}$

ɢɪᴠᴇɴ:-

• The Numerator of a fraction is 6 less than the denominator.
• If 3 is added to the numerator, the fraction becomes equal to 2/3.

ᴛᴏ ғɪɴᴅ:-

The original fraction?

ᴇxᴘʟᴀɴᴀᴛɪᴏɴ:-

Let the denominator of the fraction be x.

Then,

Numerator = x - 6

New numerator formed = x - 6 + 3 = x - 3

According to question,

$\sf\pink{↬}\dfrac{x-3}{x}$

$=\dfrac{2}{3}$

[By Cross Multiplication method]

$\sf\green{↬}3(x - 3) = 2x$

$\sf\red{↬}3x - 9 = 2x$

$\sf\purple{↬}3x - 2x = 9$

$\green{ \underline{ \boxed{ \sf{x=9}}}}$

Hence,

The denominator of the fraction is 9.

Numerator of the fraction = 9 - 6 = 3.

So, the original fraction = 3/9.

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