Question

From a jar containing milk and water
solution, 20% of the mixture is taken out
and same quantity of water was added to
the mixture. If the respective ratio
between resultant quantity of milk and
water is 32 : 15. Find the ratio of the
initial amount of milk and water?

Answer 1

Answer:

The ratio of the initial amount of milk and water, w = 40 : 7.

Step-by-step explanation:

From the above question,

They have given :

A jar containing milk and water solution, 20% of the mixture is taken out

and same quantity of water was added to the mixture. If the respective ratio between resultant quantity of milk and water is 32 : 15.

Let the quantity of milk and water in initial solution be 5m and 5w, then

Let the initial ratio of milk and water be x : y.

20% of the mixture taken out = (x+y) * 20 / 100 = 0.2 (x+y)

Quantity of water added = 0.2(x+y)

Ratio of milk and water in the resultant mixture = 32:15

Therefore, (x+0.2x+y+0.2y):(y+0.2x+0.2y) = 32:15

                  8x + 8y = 480

                   x + y = 60

The ratio of the initial amount of milk and water is x:y = 4:3.

According to question,

                   $\frac{4m}{4w + (m+w)} = \frac{32}{15}$

                  15m = 8(5w + m)

                   7m = 40w

                   m : w = 40 : 7

Hence, the required ratio = 5m : 5w = m : w = 40 : 7.

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