Question
(5n + 15) litres mixture (milk + water) contains 40% water. If (n − 3) litres water is added to the mixture, then ratio of quantity of milk to water becomes 3 : 2. Find the value of (2n − 3)².
Solution
Initial quantity of water
= 0.4 × (5n + 15) = (2n + 6) litres Initial quantity of milk
= 5n + 15 − 2n − 6 = (3n + 9) litres ATQ; After adding water → water = 2n + 6 + n − 3 = (3n + 3) So, (3n + 9) : (3n + 3) = 3 : 2 Or, 2 × (3n + 9) = 3 × (3n + 3) Or, 6n + 18 = 9n + 9 Or, 3n = 9 Or, n = 3 Required value
= (2n − 3)²
= (6 − 3)²
= 3²
= 9
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