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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