In a 50 litres mixture of milk and water volume of water is 60% total mixture. A few litres of mixture is released and an equal amount of water is added and this process is reapeted once again. If volume of water was 15% in final mixture then how many litres of mixture released each time? a) 15 b) 20 c) 25 d) 30 e) none of these.
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Step-by-step explanation:
According to the given problem,
(i) A milk and water solution has 60% of the milk mixed with water to obtain 50% of milk solution.
(ii) If 5 liters of water was poured, what is the quantity of the original solution?
(iii) Let V denotes the quantity (in liters) of the original solution.
(iv) Let (M1, W1) & (M2, W2) denote (milk, water) of the initial & final mixtures respectively.
From (i), (iii) & (iv) we get following relations,
M1 = 60% of V = 0.60*V …. (1a)
W1 = 40% of V = 0.40*V …. (1b)
M2 = M1 …. (1c) [quantity of milk same in two mixtures]
From (i), (ii) & (iv) we get following relations,
W2 = W1 + 5 …. (1d) [final mixture contains 5 liters added water]
M2 = W2 …. (1e) [final mixture contains 50% milk & 50% water]
From (1a) & (1c) we get,
M2 = 0.60*V …… (2a)
From (1b) & (1d) we get,
W2 = 0.40*V + 5 …… (2b)
Hence from (1e), (2a) & (2b) we get,
0.60*V = 0.40*V + 5
or 0.20*V = 5 or V = 5/0.2 = 25 (liters) [Ans]