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WE:Education (Education)
Re: 2/5 th of mixture of milk and water is replaced
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11 Feb 2021, 06:26
Let
Milk = M lts
Water = (M + 20) lts
Total (initial) = (2M + 20) lts
Now, \(\frac{2}{5}^{th}\) of total = \(\frac{4}{5}\)M + 8 = Orange
Therefore, In resulting mixture;
Milk = \(\frac{3}{5}\)M
Water = \(\frac{3}{5}\)M + 12
Orange = \(\frac{4}{5}\)M + 8
Also, Milk : Water : Orange = 4 : 5 : 6
i.e. Milk = 4x
Water = 5x
Orange = 6x
We can relate both the expression of Milk or Water or Orange, I am gonna take Milk here,
Milk = 4x = \(\frac{3}{5}\)M ....... (1)
Water = 5x = \(\frac{3}{5}\)M + 12 ....... (2)
Put the value of (1) in (2);
Water = 5x = 4x + 12
Therefore, x = 12
Now,
Milk = 48 lts
Water = 60 lts
Orange = 72 lts
Total = 180 lts
Currently, Milk and Orange = 48 + 72 = 120 lts
But we require it to be 66 lts
We must take out 54 lts to do so
So, % = \(\frac{54}{120}\) x 100 = 45%
Hence, option C