Bissoy.com
Doctors Medicines MCQs Q&A

In a vessel, a mixture of milk and water is in ratio 8 : 7, while in another vessel mixture of milk and water is in ratio 7 : 9. In what ratio mixture of both the vessels should be mixed together so that in the resultant mixture ratio of water and milk becomes 9 : 8?

In a vessel, a mixture of milk and water is in ratio 8 : 7, while in another vessel mixture of milk and water is in ratio 7 : 9. In what ratio mixture of both the vessels should be mixed together so that in the resultant mixture ratio of water and milk becomes 9 : 8? Correct Answer 135 : 256

Given:

The ratio of milk and water in the first vessel = 8 : 7

The ratio of milk and water in the second vessel = 7 : 9

The ratio of water and milk in the resultant mixture = 9 : 8

Calculation:

Let x litre of the first mixture and y litre of the second mixture are mixed.

Quantity of milk in x litre of the first mixture = 8x/15

Quantity of milk in y litre of the second mixture = 7y/16

Total quantity of the resultant mixture = (x + y)

Quantity of milk in (x + y) litre of the resultant mixture = 8(x + y)/17

8x/15 + 7y/16 = 8(x + y)/17

⇒ 8x/15 + 7y/16 = 8x/17 + 8y/17

⇒ 8x/15 – 8x/17 = 8y/17 – 7y/16

⇒ (136x – 120x)/15 × 17 = (128y – 119y)/17 × 16

⇒ 16x/15 = 9y/16

⇒ 256x = 135y

⇒ x/y = 135/256

∴ The required ratio is 135 : 256

Alternative Method:

The concentration of milk in the first mixture = 8/15

The concentration of milk in the second mixture = 7/16

The concentration of milk in the resultant mixture = 8/17

By the rule of Allegation,

[ alt="F1 Ashish 4.12.20 Pallavi D11" src="//storage.googleapis.com/tb-img/production/20/12/F1_Ashish_4.12.20_Pallavi_D11.png" style="width: 365px; height: 131px;">

⇒ 9/272 : 16/255

⇒ 9 × 255 : 16 × 272

⇒ 9 × 15 : 16 × 16

⇒ 135 : 256     

∴ The required ratio is 135 : 256.

Related Questions

In a vessel, a mixture of milk and water is in ratio 9 : 2, while in another vessel mixture of milk and water is in ratio 7 : 5. In what ratio mixture of both the vessels should be mixed together so that in the resultant mixture ratio of water and milk becomes 3 : 8?
There are two vessels A and B. Vessel A is containing 60L of Pure milk and vessel B is containing 28L of pure water. From vessel A, 8L 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 milk in vessel A to the quantity of pure water in vessel B?
First vessel contains mixture of milk and water in ratio of 1 ∶ 3. Second vessel contains mixture of milk and water in ratio of 4 ∶ 5. When this mixtures are mixed then ratio of milk and water in resultant mixture is 11 ∶ 19. Find the quantity of mixture mixed from First vessel if resultant mixture is of 60 litres.
Each question below is followed by two statements I and II. You have to determine whether the data given in the statements are sufficient for answering the question. You should use the data and your knowledge of Mathematics to choose the best possible answer. What is the ratio of coconut oil and milk in the final beaker? If contents from four vessels poured in it. I. Vessel B has 10 ml more capacity than vessel A and the ratio of coconut oil and milk in vessel B is 2 ∶ 7. Vessel C has coconut oil and milk in the ratio 2 ∶ 3 and contains 38 ml more capacity than Vessel D II. Vessel A has milk and coconut oil in the ratio 3 ∶ 5. Vessel C has 12 ml more coconut oil than vessel D.
There are three vessels A, B and C having milk to water ratio as 3 : 5, 1 : 3 and 7 : y.  After adding mixture of vessel B to A, the milk to water ratio becomes 1 : 2 in A. Now 60% of mixture is taken out from vessel A and mixture of vessel C is mixed with remaining mixture of vessel A which results in a final milk to water ratio of 3 : 4. Find the value of y given that volume of B is 20 litres and volume of C is (7 + y) lires
Two vessels contain a mixture of milk and water. In the first vessel, the ratio of milk and water is 5 : 2 and in the second vessel, the ratio is 8 : 5. A 54 L vessel is filled from these vessels so as to contain a mixture of milk and water in the ratio of 9 : 4. How many litres are taken from the first vessel?
Two vessels contain a mixture of milk and water. In the 1st vessel, the ratio of milk and water is 8 ∶ 3 and in the 2nd vessel, this ratio is 5 ∶ 1. A big vessel of capacity 35 L is filled with these vessels so as to contain the mixture of milk and water in the ratio 4 ∶ 1. How many litres are taken from the 1st vessel?
Two vessels A and B contain a mixture of acid and Water. In vessel A the ratio of acid and water is 2 ∶ 1 and in vessel B the ratio is 5 ∶ 1.Mixture from these two vessels are filled in another 42 litre vessel to contain a mixture of acid and water in the ratio of 5 ∶ 2. How much mixture is taken from vessel A?
The three vessels are X, Y, and Z. The ratio of ingredients A and B in vessel X is 6 : 5, the ratio of ingredients B and C in vessel Y is 7 : 4 and the ratio of ingredients C and A to vessel Z is 3: 8, the mixture of the three vessels is mixed in a ratio of 2 : 5 : 8  and placed in a new vessel P, then what is the percentage of ingredient B in the new vessel? (near to two decimal points)
In one vessel there is the mixture of milk and water in the ratio 5 : 2 and in another the ratio of milk and water is 4 : 3. The quantity of mixture in the other vessel is double the quantity of the mixture in the first vessel. If both the mixtures are poured in a single vessel, what will be the ratio of milk and water in the new mixture?