Question : There are three cups of milk and water in ratios 4 : 5, 5 : 6, 9 : 7. 36 litres of the first and 44 litres of the second cup are taken. How much quantity from the third cup is to be taken so that the final mixture from the three cups will have milk and water in a ratio 1 : 1?
Option 1: 32 litres
Option 2: 64 litres
Option 3: 54 litres
Option 4: 60 litres
Correct Answer: 64 litres
Solution :
Given: There are three cups of milk and water in ratios 4 : 5, 5 : 6, 9 : 7.
In the first mixture of 36 litres, the quantity of milk = $36×\frac{4}{4+5}=36×\frac{4}{9}=16$ litres
So, the quantity of water in the first mixture = 36 – 16 = 20 litres
In the 2nd mixture of 44 litres, the quantity of milk = $44×\frac{5}{5+6}=44×\frac{5}{11}=20$ litres
So, the quantity of water in the 2nd mixture = 44 – 20 = 24 litres
Let the quantity of milk drawn from the third cup be $9x$ and the water quantity is $7x$.
According to the question,
$\frac{16+20+9x}{20+24+7x}=\frac{1}{1}$
$⇒36+9x=44+7x$
$\therefore x =4$
Quantity of mixture in the third cup = $9x+7x=16x=16×4=64$ litres
Hence, the correct answer is 64 litres.
Related Questions
Know More about
Staff Selection Commission Multi Tasking ...
Application | Cutoff | Selection Process | Preparation Tips | Eligibility | Exam Pattern | Admit Card
Get Updates BrochureYour Staff Selection Commission Multi Tasking Staff Exam brochure has been successfully mailed to your registered email id “”.