The denominator of a fraction is greater than its numerator by 11. If 8 is added to both its numerator and denominator, it becomes . Find the fraction.
Answers
Let the required fraction be x/y . Then, we have: y = x + 11 ⇒ y – x = 11 ……(i) Again, x+8 /y+8 = 3/4 ⇒4(x + 8) = 3(y + 8) ⇒4x + 32 = 3y + 24 ⇒ 4x – 3y = -8 ……(ii) On multiplying (i) by 4, we get: 4y – 4x = 44 On adding (ii) and (iii), we get: y = (-8 + 44) = 36 On substituting y = 36 in (i), we get: 36 – x = 11 ⇒ x = (36 – 11) = 25 ∴ x = 25 and y = 36 Hence, the required fraction is 25/36 .Read more on Sarthaks.com - https://www.sarthaks.com/132534/denominator-fraction-greater-than-numerator-added-both-numerator-denominator-becomes?show=132541#a132541
Answer:
Let the required fraction be x/y . Then, we have: y = x + 11 ⇒ y – x = 11 ……(i) Again, x+8 /y+8 = 3/4 ⇒4(x + 8) = 3(y + 8) ⇒4x + 32 = 3y + 24 ⇒ 4x – 3y = -8 ……(ii) On multiplying (i) by 4, we get: 4y – 4x = 44 On adding (ii) and (iii), we get: y = (-8 + 44) = 36 On substituting y = 36 in (i), we get: 36 – x = 11 ⇒ x = (36 – 11) = 25 ∴ x = 25 and y = 36 Hence, the required fraction is 25/36 .Read more on Sarthaks.com - https://www.sarthaks.com/132534/denominator-fraction-greater-than-numerator-added-both-numerator-denominator-becomes