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CAT 2021 Slot 2 QA Question & Solution

ArithmeticMedium

Question

From a container filled with milk, 9 litres of milk are drawn and replaced with water. Next, from the same container, 9 litres are drawn and again replaced with water. If the volumes of milk and water in the container are now in the ratio of 16 : 9, then the capacity of the container, in litres, is

Solution

Let initial volume be V, final be F for milk.

The formula is given by : $F\ =\ V\cdot\left(1-\frac{K}{V}\right)^n$ n is the number of times the milk is drawn and replaced.

so we get $F=\ V\left(1-\frac{K}{V}\right)^{^2}$
here K =9
we get
$\frac{16}{25}V\ =\ V\ \left(1-\frac{9}{V}\right)^{^2}$
we get $1-\frac{9}{V}=\ \frac{4}{5}or\ -\frac{4}{5}$

If considering $1-\frac{9}{V}=-\frac{4}{5}$

V =5, but this is not possible because 9 liters is drawn every time.

Hence : $1-\frac{9}{V}=\frac{4}{5},\ V\ =\ 45\ liters$