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CAT 2019 Set-1 | Question: 88

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

  1. $85$
  2. $70$
  3. $75$
  4. $80$

 

1 Answer

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$\textbf{First Method:}$

Given that,

  • One litre of liquid $1$ weighs $ = 1 \; \text{kg} = 1000 \; \text {gm}.$
  • One litre of liquid $2$ weighs $ = 800 \; \text{gm}.$
  • And half litre of mixture weighs $ = 480 \; \text{gm}.$

When both liquids given and mixture also given, we can use the alligation method.

 Half litre of mixture weighs is $ 480 \; \text{gm}.$

Therefore, the weighs of liquid $1$ and liquid $2$ also become half.

Now, we can apply the alligation method.

$\therefore$ Percentage of liquid $1$ in the mixture $ = \frac{4}{5} \times 100 = 80\%.$

$ \textbf{Second Method}:$

$1$ litre mixture weigh is $480 \times 2 = 960 \text{gm}.$

$\therefore$ Percentage of liquid $1$ in the mixture $ = \frac{4}{5} \times 100 = 80\%.$

Correct Answer $: \text{D}$

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