Alligation Or Mixture Ques 18
Question
There was 120 litres of pure milk in a vessel. Some quantity of milk was taken out and replaced with 23 litres of water in such a way that the resultant ratio between the quantities of milk and water in the mixture was $4: 1$ respectively. Again 23 litres of the mixture was taken out and replaced with 27 litres of water. What is the respective ratio of milk and water in the resultant mixture?
(1) $58: 37$
(2) $116: 69$
(3) $69: 43$
(4) $101: 37$
(5) $368: 227$
(BOB Junior Management Grade/Scale-I Exam. 18.04.2015)
Show Answer
Answer: (5)
Solution: (5)
Let $x$ litres of milk was taken out firstly.
$\therefore \frac{120-x}{23}=\frac{4}{1}$
$\Rightarrow 120-x=92$
$\Rightarrow x=120-92=28$ Litres
$\therefore$ Quantity of milk $=120-28=92$ litres
Quantity of water $=23$ litres
Case II
In 23 litres of mixture,
Milk $=\frac{4}{5} \times 23=\frac{92}{5}$ litres
Water $=\frac{23}{5}$ Litres
$\therefore$ Remaining milk $=92-\frac{92}{5}=\frac{460-92}{5}$ $=\frac{368}{5}$ Litres
Quantity of water $=23-\frac{23}{5}+27$ $=\frac{115-23+135}{5}=\frac{227}{5}$ litres
$\therefore$ Required ratio $=\frac{368}{5}: \frac{227}{5}$ $=368: 227$
BETA
