Question

A vessel is filled to its capacity with pure milk. Ten litres are withdrawn from it and replaced by water. This procedure is repeated again. The vessel now has 32 litres of milk. Find the capacity of the vessel.

Answer 1

x (1- 10/x)^2 = 32
x^2 +100-20x = 32x
x^2 +100 +52x= 0
x^2 + 50x + 2x + 100 = 0
x= 50 

Answer 2

Answer:

50 liters

Step-by-step explanation:

Let the volume of vessel be x

We are given that Ten liters are withdrawn from it and replaced by water.

Rate = $\frac{10}{x}$

This procedure is repeated again.

Formula : $a(1-r)^n$

So, $x(1-\frac{10}{x})^2 =32$

$x^2 +100-20x = 32x$

$x^2 +100 -52x= 0$

$x^2 -50x - 2x + 100 = 0$

$x(x-50) -2(x - 50) = 0$

$x=2,50$

Hence the capacity of the vessel is 50 liters