Question

There are two vessels A and B. Vessel A is containing 40 L of pure milk and vessel B is containing 22 L of pure water . From vessel A, 8 L of milk is taken out and poured into vessel B. Then, 6L of mixture (milk and water) is taken out from vessel B and poured into vessel A. What is the ratio of the quantity of pure milk in vessel A to the quantity of pure water in vessel B?

• A. 14 : 9
  
• B. 21 : 11
  
• C. 24:13
  
• D. 14 : 5
  
• E. 21 : 13

Answer 1

The correct option is B 21 : 11


Initial quantity of milk in vessel A = 40 L
Initial quantity of water in vessel 8 = 22 L
Now, 8 L of milk is poured to vessel B.
$\therefore$ Quantity of milk left in vessel,
A=40-8 =32 L
$\because$ Quantity of milk in vessel B =8 L and quantity of water in vessel B =22 l
$\therefore$ (Milk : water ) in vessel
B =8 : 22 =4 : 11
Now, 6 L of mixture (milk and water) is taken out from vessel B and poured into vessel A.
$\therefore$ Quantity of milk in 6 L
$=6\times \frac{4}{15}=\frac{2\times 4}{5}=\frac{8}{5}$
and quantity of water in 6 L
$=6\times \frac{11}{15}=\frac{2\times 11}{5}=\frac{22}{5}$
Now, quantity of milk in vessel A
$=32+\frac{8}{5}=\frac{168}{5}$
and quantity of water in vessel B
$=22-\frac{22}{5}=\frac{88}{5}$
$\therefore$ Required ratio $=\frac{168}{5}:\frac{88}{5}$
=168 : 88 = 21 : 11