If a mixture contains honey and water both in an integral number of liters. When 91L of water is added to the mixture the ratio becomes square of the initial ratio. What was the initial ratio of honey and water?
Answers
Answer:
the initial ratio of honey and water = 6 : 13
actual content = 36 & 78 litre
Step-by-step explanation:
Let say Ratio is
H : W
Let say actually quantity of honey & water
= HK & WK
Now 91 Litre water is added
=> New Ratio
HK : (WK + 91)
(H/W)² = HK : (WK + 91)
=> H (WK + 91) = KW²
=> HWK + 91H = KW²
=> KW(W - H) = 91H
91 = 7 * 13
=> W - H = 7 or 13
Case 1 W - H = 13
=> K(13 + H)(13) = 91H
=> 13K + HK = 7H
=> 13K = H(7 - K)
7 - K ≠ 13
Case 2 W - H = 7
=> K(7 + H)(7) = 91H
=> 7K + HK = 13H
=> 7K = H(13 - K)
13 - K = 7
=> K = 6
HWK + 91H = KW²
=> 6WH + 91H = 6W²
=> 6W² - 6WH = 91H
=> 6W(W - H) = 91 H
=> 6W(W - H) = 13 * 7 * H
W = 13 & H = 6 satisfy equation
=> H:W :: 6 : 13
36 & 78 litre actual content
Step-by-step explanation:
x:y---x²:xy
x²:y²
xy+91 = y²
91 = y(y-x)
7*13 = y(y-x)
y = 13 , x = 6
6:13