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From a container full of milk, 10 liters (l) was drawn and replaced by water. This process is repeated one more time. The ratio of quantity of milk and water left in the container is 4:5. Then the capacity of the container is:

Solution

✅ Correct Option: 3

Let the capacity of the container =C= C liters.

The milk left after nn operations is given by:

Milk left=C×(1−10C)n\text{Milk left} = C \times \left(1 - \dfrac{10}{C}\right)^n


The milk to water ratio is 4:54:5, so:

Milk left=44+5×C\text{Milk left} = \dfrac{4}{4+5} \times C

=49×C= \dfrac{4}{9} \times C


Using the formula with n=2n = 2:

C×(1−10C)2=49×CC \times \left(1 - \dfrac{10}{C}\right)^2 = \dfrac{4}{9} \times C

(1−10C)2=49\left(1 - \dfrac{10}{C}\right)^2 = \dfrac{4}{9}

1−10C=231 - \dfrac{10}{C} = \dfrac{2}{3}

10C=1−23\dfrac{10}{C} = 1 - \dfrac{2}{3}

10C=13\dfrac{10}{C} = \dfrac{1}{3}

C=30C = 30


The capacity of the container =30= 30 liters.

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