Question

In the given question,20 litres of a mixture contains milk and water in the ratio $5:3$. If 4 litres of this mixture is replaced by 4 liter of milk, the ratio of milk in the new mixture would be

a.$2:1$

b.$7:3$

c.$8:3$

d.$4:3$

Answer 1

Hint: Water was not added in the new mixture. So, the quantity of water in the new mixture is the same.

Complete step-by-step answer:
Let the amount of milk and water in a 20 litres mixture is $5x$ and $3x$.
If 4 liter of mixture is replaced by 4 liter of milk, then we have
Milk = 5x+4 and water = 3x
According to the given condition,
$5x + 4 + 3x = 20$
$8x + 4 = 20$
$8x = 20 - 4$
$8x = 16$
$x = 2$
Now, consider the ratio $(R) $ of milk and water
$R = \dfrac{{5x + 4}}{{3x}}............ (1)$
Put $x = 2$ in the equation (1), we get
$R = \dfrac{{5(2) + 4}}{{3(2)}} = \dfrac{{10 + 4}}{6} = \dfrac{{14}}{6}$
$R = \dfrac{7}{3}$
Thus, the ratio $(R) $ of milk and water in the new mixture is $7:3$.
Hence, the correct option of the given question is option (b).

Note: Alternatively this question is solved as follows-
Given that, 20 litres of mixture contains milk and water.
Ratio of milk and water is $5:3$ and hence milk $ = \dfrac{5}{8}$.
Now, 4 liter of mixture is replaced by milk. So, total mixture available = 20 – 4 = 16 litres.
The quantity of milk in a 16 litres mixture = $16 \times \dfrac{5}{8} = 2 \times 5 = 10$ litres.
The quantity of milk in 20 litres new mixture = (10 + 4) = 14 litres.
The quantity of water in new mixture = (20–14) = 6 litres
Thus, the ratio of milk and water in the new mixture =$14:6 = 7:3$.
Hence, the correct option of the given question is option (b).