Question : In a mixture of 178 litres, the ratio of water and milk is 5 : 7. How much water should be added to make the ratio of water and milk 3 : 4?
Option 1: $3 \frac{17}{24}$ litres
Option 2: $3 \frac{13}{24}$ litres
Option 3: $2\frac{11}{24}$ litres
Option 4: $2\frac{23}{24}$ litres
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Correct Answer: $3 \frac{17}{24}$ litres
Solution :
Total quantity = 178 litres
Quantity of water = $178 \times \frac{5}{12} = \frac{890}{12}$ litres
Quantity of milk = $178 \times \frac{7}{12} = \frac{1246}{12}$ litres
Now, after adding $x$ litres of water.
$⇒\frac{\frac{890}{12} + x}{\frac{1246}{12}} = \frac{3}{4}$
$⇒\frac{\frac{890+12x}{12}}{ \frac{1246}{12}} = \frac{3}{4}$
$⇒\frac{890+12x}{1246} = \frac{3}{4}$
$⇒4(890+12x)= 3 \times 1246$
$⇒3560+48x= 3738$
$⇒48x= 178$
$⇒x = 3\frac{34}{48} = 3\frac{17}{24}$ litres
Hence, the correct answer is $3\frac{17}{24}$ litres.
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