The Milk and Water in Two Vessels A and B are in the Ratio 4:3 and 2:3 GMAT Problem Solving

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?

  1. 8 : 3
  2. 7 : 5
  3. 4 : 3
  4. 2 : 3
  5. 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p litres of 3p/7 water were withdrawn from vessel A.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.


Suggested GMAT Problem Solving Questions

Fees Structure

CategoryState
General15556

In case of any inaccuracy, Notify Us! 

Comments


No Comments To Show