Arithmetic

Numericals

Easy

applied

A mixture contains apple juice and water in the ratio $10: \mathrm{x}$ . When $36$ litres of the mixture and $9$ litres of water are mixed, the ratio of apple juice and water becomes $5: 4$ . The value of $x$ is :

$4$

$4.4$

$5$

$8$

✅ Correct Option: 2

Let the ratio of apple juice to water be $10:x$ .

In 36 L of the mixture: $\text{Apple juice}=\dfrac{10}{10+x}\times36$

$\text{Water}=\dfrac{x}{10+x}\times36$

After adding 9 L of water, the ratio becomes $5:4$ : $\dfrac{\dfrac{360}{10+x}}{\dfrac{36x}{10+x}+9}=\dfrac54$

Cross-multiplying: $1440=180x+45(10+x)$

$1440=225x+450$

$225x=990$

$x=\dfrac{22}{5}=4.4$

Answer: ${x=4.4}$

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A mixture contains apple juice and water in the ratio 10:x10: \mathrm{x}10:x. When 363636 litres of the mixture and 999 litres of water are mixed, the ratio of apple juice and water becomes 5:45: 45:4. The value of xxx is :