Difference of numerator and denominator of a proper fraction is 2. If 3 is subtracted from numerator and 3 is added to denominator of the fraction it will be equal to 1/5. Find the fraction?

Question: Difference of numerator and denominator of a proper fraction is 2. If 3 is subtracted from numerator and 3 is added to denominator of the fraction it will be equal to 1/5. Find the fraction?

Solution:
ধরি,
ভগ্নাংশের লব = x
ভগ্নাংশের হর = x + 2

ভগ্নাংশটি = x/(x + 2)

প্রশ্নমতে,
(x - 3)/(x + 2 + 3) = 1/5
⇒ (x - 3)/(x + 5) = 1/5
⇒ 5x - 15 = x + 5
⇒ 5x - x = 15 + 5
⇒ 4x = 20
⇒ x = 5

∴ ভগ্নাংশটি = 5/(5 + 2) = 5/7