Question: There are two vessels A and B. Vessel A is containing 40 litres of pure milk and vessel B is containing 22 litres of pure water. From vessel A, 8 litres of milk is taken out the poured into vessel B. Then 6 litres of mixture (milk and water) is taken out the from vessel B 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) 24 : 17
(B) 13 : 7
(C) 21 : 11
(D) 14 : 5
(E) 3 : 1

Correct Answer: C

Solution and Explanation:

Approach Solution 1:
From vessel A, 8 litres of milk is taken out the poured into vessel B:

Now vessel A has 32 L of milk. Vessel B has 8 L milk and 22 L water, hence 30 L of 8/30=4/15 percent milk.
Then 6 litres of mixture (milk and water) is taken out the from vessel B poured into vessel A:
This is one-fifth of vessel B taken out; among that we have 6∗4/15= 8/5= 1.6 L milk and 6−1.6= 4.4 L water.
Then vessel A has 32 + 1.6 = 33.6 L of milk. Vessel B has 22 - 4.4 = 17.6 L of water.
33.6:17.6= 168:88= 21:11

Approach Solution 2:
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.
∴ Quantity of milk left in vessel,
A=40-8 =32 L
∵ Quantity of milk in vessel B =8 L and quantity of water in vessel B =22 l
∴(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.
∴Quantity of milk in 6 L= 6*4/15
= 2*4/5= 8/5
and quantity of water in 6 L
= 6*11/15= 2*11/5= 22/5
Now, quantity of milk in vessel A
= 32+8/5= 198/5
and quantity of water in vessel B
= 22-22/5= 88/5
∴Required ratio= 168/5 : 88/5
=168 : 88 = 21 : 11

Approach Solution 3:
The quantity in vessel B after 8 litre milk is poured in it= 22+8= 30 litres
Quantity of milk in vessel A= 40-8= 32 litres
In 6 litres of mixture from vessel B, milk contained is = 6*8/20= 8/5
Water= 6*22/20= 22/5
Pure milk in A= 32+8/5= 168/5
Pure water in B= 22-22/5= 88/5
Pure milk in A: Pure water in B
= 168:88
= 21:11

“There are two vessels A and B. Vessel A is containing 40 litres of”- is a topic of the GMAT Quantitative reasoning section of GMAT. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. GMAT Quant practice papers improve the mathematical knowledge of the candidates as it represents multiple sorts of quantitative problems.

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