Question

A chemist mixed an acid of 48% concentration with the same acid of 80% concentration, and then added 2 litres of distilled water to the mixed acid. As a result, he got 10 litres of the acid of 40% concentration. How many
millilitre of the acid of 48% concentration that the chemist had used? (1 litre = 1000 millilitres)​

Answer 1

Answer:

7500 ml

Step-by-step explanation:

The total volume of the mixture is 10 liters.

If the volume of the acid with 48% concentration is x liters and that of the acid with 80% concentration is y liters, then  

x + y = 10 - 2 = 8 ........ (1) {Since 2 liters of distilled water is added to the mix}

If the final mix is of 40% concentration, then we can write

$\frac{0.48x + 0.8 y}{x + y +2} = \frac{40}{100}$

⇒ 0.48x + 0.8y = 0.4x + 0.4y + 0.8

⇒ 0.08x + 0.4y = 0.8

⇒ 8x + 40y = 80

⇒ x + 5y = 10 ....... (2)

Now, solving equations (1) and (2) we get,

8 - y + 5y = 10, ⇒ 4y = 2, ⇒ y = 0.5 liters

Hence, from equation (1), x = 8 - 0.5 = 7.5 liters.

Therefore, 7.5 liters i.e. 7500 milliliters of 48% acid was used. (Answer)