A chemist mixes two liquids $1$ and $2$ . One litre of liquid $1$ weighs $1 \mathrm{~kg}$ and one litre of liquid $2$ weighs $800 \mathrm{gm}$ . If half litre of the mixture weighs $480 \mathrm{gm}$ , then the percentage of liquid $1$ in the mixture, in terms of volume, is

$80$

$75$

$85$

$70$

✅ Correct Option: 1

We have two liquids with different densities being mixed, and we need to find what percentage of the mixture is liquid 1 by volume.

Given Information:

1 litre of liquid 1 weighs 1 kg = 1000 gm

1 litre of liquid 2 weighs 800 gm

Half litre of the mixture weighs 480 gm

For liquid 1: If 1 litre weighs 1000 gm, then half litre weighs 500 gm

For liquid 2: If 1 litre weighs 800 gm, then half litre weighs 400 gm

We'll use the Alligation Method - a technique used when two quantities of different concentrations/densities are mixed. It helps us find the ratio in which they should be mixed to get a desired result.

The mixture weighs 480 gm for half litre, which is between 400 gm (liquid 2) and 500 gm (liquid 1).

Liquid 1 (500 gm)    Mixture (480 gm)    Liquid 2 (400 gm)
        \                   |                   /
         \                  |                  /
          \                 |                 /
           \________________|________________/
                |480 - 400| : |500 - 480|
                     80     :     20
                     4      :     1

In alligation, we find how far each liquid's weight is from the mixture's weight. The ratio is inversely proportional to these differences.

The ratio of liquid 1 to liquid 2 is 4:1

This means out of every 5 parts of the mixture:

4 parts are liquid 1

1 part is liquid 2

Percentage of liquid 1 = $\dfrac{4}{4+1} \times 100 = \dfrac{4}{5} \times 100 = 80\%$

Therefore, liquid 1 makes up 80% of the mixture by volume.

Alligation is extremely useful for mixture problems. Remember that the ratio is always inverse to the differences from the mean!

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A chemist mixes two liquids $1$ and $2$ . One litre of liquid $1$ weighs $1 \mathrm{~kg}$ and one litre of liquid $2$ weighs $800 \mathrm{gm}$ . If half litre of the mixture weighs $480 \mathrm{gm}$ , then the percentage of liquid $1$ in the mixture, in terms of volume, is