In a mixture, milk and water are in ratio of 2:3. Some milk is added to the mixture because of which ratio of milk and water become 10:3. How much milk was added as a percentage of initial mixture ?

a) 160 percentage
b) 140 percentage
c) 100 percentage
d) 120 percentage

Ans : a) 160 percentage

SSC Constable GD Paper : 21 Feb 2024 (1st shift)

Solution

Initial ratio of milk to water = 2:3
Final ratio of milk to water after adding some milk = 10:3

Let:

The initial quantity of milk = ( 2x )
The initial quantity of water = ( 3x )

Initial total mixture:

Total initial mixture = ( 2x + 3x = 5x )

After adding some milk:

Let the quantity of milk added be ( y ).
New quantity of milk = ( 2x + y )
Quantity of water remains the same = ( 3x )

According to the problem:

$\frac{2x + y}{3x} = \frac{10}{3}$

Cross-multiply and solve for ( y ):

3(2x + y) = 10(3x)
6x + 3y = 30x
3y = 24x
y = 8x

So, the amount of milk added is ( 8x ).

Percentage of milk added relative to the initial mixture:

$\text{Percentage} = \left(\frac{y}{\text{Initial total mixture}}\right) \times 100$
$\text{Percentage} = \left(\frac{8x}{5x}\right) \times 100 = \frac{8}{5} \times 100 = 160\%$

Answer: The milk added is 160% of the initial mixture.