A fraction becomes 1/2 when 1 is added to both numerator and denominator.It becomes 1/3 when 2 is subtracted from both numerator and denominator. what is the fraction?
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Answer:
fraction to be x and the denominator of the fraction to be y. So, the required fraction is xyxy From the question it’s given as, If 1 is subtracted from both numerator and the denominator, the fraction becomes 1313. Thus, the equation so formed is, (x–1)(y−1)(x–1)(y−1) = 1313 ⇒ 3(x–1) = (y–1) ⇒ 3x – 3 = y – 1 ⇒ 3x – y – 2 = 0…. (i) And also it’s given in the question as, If 1 is added to both numerator and the denominator, the fraction becomes 1212. Expressing the above condition in an equation, we have (x+1)(y+1)(x+1)(y+1) = 1212 ⇒ 2(x+1) = (y+1) ⇒ 2x + 2 = y + 1 ⇒ 2x – y + 1 = 0 …….. (ii) Solving (i) and (ii), to find the fraction By using cross-multiplication, we have ⇒ x = 3, y = 7 Hence, the required fraction is 3737.Read more on Sarthaks.com - https://www.sarthaks.com/632884/a-fraction-becomes1-3if-1-is-subtracted-from-both-its-numerator-and-denominator