Question

Question :

the numerator of a certain fraction is 8 less than the denominator. If 3 is added to the numerator and 3 is subtracted from the denominator, the fraction becomes 3/4. Find the original fraction.​

Answer 1

Let the values,

Numerator = ( X - 8 )

Denominator = X

Fraction = Numerator/Denominator = ( X -8)/X.

When 3 is added to the numerator and 3 is subtracted from the denominator the fraction obtained is 3/4

X - 8 + 3 / X - 3 =3 /4

X-5/X-3 = 3/4

4X-20 = 3X-9

X = 11

So,(X-8)/X = (11-8)/11

Answer is 3/11

Answer 2

◈ɢɪᴠᴇɴ:-

• The numerator of a fraction is 8 less than it's denominator
• If 3 is added to the numerator and 3 is subtracted from the denominator, the fraction becomes 3/4

◈ᴛᴏ ғɪɴᴅ:-

• The original fraction

◈sᴏʟᴜᴛɪᴏɴ:-

Let the numerator and the denominator be:-

• Numerator be 'x'

❐ As per the given question the numerator is 8 less than the denominator

• Denominator be 'x+8'

So, the fraction we get by the above conditions

$\large \sf \green \leadsto{ \frac{x}{x + 8} }$

❐When 3 is added to the numerator and 3 is subtracted from the denominator it becomes:-

$\large \sf \green \leadsto{ \frac{x + 3}{x + 8 - 3} } = \frac{x + 3}{x + 5}$

Now ATQ:-

$\large\sf \green \leadsto{ \frac{x + 3}{x + 5} } = \frac{3}{4}$

(By cross multiplication)

$\sf \green \leadsto{4(x + 3) = 3(x + 5)}$

$\sf \green \leadsto{4x + 12 = 3x + 15}$

$\sf \green \leadsto{4x - 3x = 15 - 12 \: (by \: transposing)}$

$\sf \green \leadsto{x = 3}$

• The numerator is x = 3
• The denominator is x + 8 = 3+8= 11

So,the original fraction is $\sf\large{\frac{3}{11}}$