Question
(5n + 30) litres mixture (milk + water) contains 40% water. If (n − 6) litres water is added to the mixture, then ratio of quantity of milk to water becomes 6 : 5. Find the value of (n + 2)².
Solution
Initial quantity of water
= 0.4 × (5n + 30) = (2n + 12) litres Initial quantity of milk
= 5n + 30 − 2n − 12 = (3n + 18) litres ATQ; Water after addition = 2n + 12 + n − 6 = (3n + 6) So, (3n + 18) : (3n + 6) = 6 : 5 Or, 5 × (3n + 18) = 6 × (3n + 6) Or, 15n + 90 = 18n + 36 Or, 3n = 54 Or, n = 18 Required value
= (n + 2)²
= (18 + 2)²
= 20²
= 400
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