Question
26.75 litres of a mixture P (milk and water) is combined
with another mixture Q. The resulting mixture has milk to water in the ratio 4:7. If mixture Q has 8.2 litres more milk and 20.1 litres more water than mixture P, find the approximate amount of water in mixture Q.Solution
ATQ,
Let the quantity of milk and water in mixture P be a litres and b litres, respectively. Then, mixture Q contains (a + 8) litres of milk and (b + 20) litres of water. Now, (a + a + 8)/(b + b + 20) ≈ 4/7 (2a + 8)/(2b + 20) ≈ 4/7 → 7(2a + 8) = 4(2b + 20) → 14a + 56 = 8b + 80 → 14a – 8b ≈ 24 ...... (1) Also, a + b ≈ 27 ...... (2) Solving (1) and (2), a = 10 litres, b = 17 litres So, approximate quantity of water in mixture Q = 17 + 20 = 37 litres
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