Question: The milk and water in two vessels A and B are in the ratio 4:3 and 2:3 respectively. In what ratio the liquids in both the vessels be mixed to obtain a new mixture in vessel c consisting half milk and half water?
- 8 : 3
- 7 : 5
- 4 : 3
- 2 : 3
- 1 : 3
Correct Answer: B
Solution and Explanation
Approach Solution 1:
The liquid in both vessels should be blended at a p:q ratio.
P litres was poured from vessel A.
Q litre was poured from vessel B.
Water to milk in vessel A is 4:3.
Water to milk in vessel B is 2:1.
Milk to water ratio should be 1:1.
p litres of 4p/7 milk were taken out of vessel A.
q litre, or 2 q/5 milk, was taken out of vessel B.
p litres of 3p/7 water were withdrawn from vessel A.
q litres of water, or 3 q/5 water, were removed from vessel B.
(4p/7+2q/5):(3p/7+3q/5) = 1:1
So p:q =7:5
Approach Solution 2:
There is another approach to answering this question:
In consideration of the stated problem,
(i) The ratios of the two vessels P & Q in milk and water are 4:3 and 2:3, respectively.
(ii) In order to create a new mixture in vessel R that contains half milk and half water, what ratio of the liquid in both vessels P & Q is mixed?
(iii) Define (milk, water) of vessels P & Q, respectively, as (MP, WP) & (MQ, WQ).
We obtain the following relations from I (ii), and (iii).
MP/WP = 4/3 (1a) [vessel P]
MQ/WQ = 2/3 (1b) [vessel Q]
MP + MQ = WP + WQ (1c) [vessel R]
From (1a) we get, MP + WP = (7/3)*WP (2a)
From (1b) we get, MQ + WQ = (5/3)*WQ (2b)
From 3*(1c) we get,
3*MP + 3*MQ = 3*WP + 3*WQ
or 4*WP + 2*WQ = 3*WP + 3*WQ [from (1a) & (1b)]
or WP = WQ …… (2c)
From (2a) & (2b) we get,
(MP + WP)/(MQ + WQ) = (7/5)*(WP/WQ) = 7/5 [from (2c)]
or (MP + WP) : (MQ + WQ) = 7 : 5
As a result, the liquids in vessels P and Q should be combined 7:5 to create a new mixture that contains half milk and half water.
Approach Solution 3:
Distance from A to C = 114114
Distance from B to C = 110110
The ratio in which the mixture needs to be mixed is given by the reverse of ratio of distance.
So, A:B = 110110/114114
A:B = 7:5
“The milk and water in two vessels A and B are in the ratio 4:3 and 2:3”- 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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