Two vessels A & B contain spirit & water mixed in the ratio 5:2 & 7:6 respectively. Find the ratio in which these mixture be mixed to obtain a new mixture in vessel C containing spirit & water in the ratio 8:5?Options :4:33:45:67:9

This problem can be solved using the rule of alligation. The alligation method is a simplified process to solve the problems related to mixtures and their ratios.

Step 1: Identify the ratios of spirit to water in vessels A and B.

Vessel A = 5:2 = 5/7 (spirit fraction) Vessel B = 7:6 = 7/13 (spirit fraction)

Step 2: Identify the ratio of spirit to water in the final mixture in vessel C.

Vessel C = 8:5 = 8/13 (spirit fraction)

Step 3: Use the rule of alligation to find the ratio in which the mixtures from vessels A and B should be mixed.

The rule of alligation states that:

(Quantity of cheaper/Quantity of dearer) = (CP of dearer - Mean Price)/(Mean Price - CP of cheaper)

Here, the 'cheaper' and 'dearer' terms refer to the mixtures with less and more spirit fraction respectively.

So,

(Quantity of mixture from A/Quantity of mixture from B) = (7/13 - 8/13) / (8/13 - 5/7)

Solving this gives us the ratio in which the mixtures should be mixed.

Please note that the ratios are not among the options provided. There might be a mistake in the problem or the options.

This problem can be solved using the rule of alligation. The alligation method is a simplified process to solve the problems related to mixtures and their ratios.

Step 1: Identify the ratios of spirit to water in vessels A and B.

Vessel A = 5:2 = 5/7 (This is the fraction of spirit in the mixture) Vessel B = 7:6 = 7/13 (This is the fraction of spirit in the mixture)

Step 2: Identify the ratio of spirit to water in vessel C.

Vessel C = 8:5 = 8/13 (This is the fraction of spirit in the mixture)

Step 3: Use the rule of alligation.

The rule of alligation states that:

(Cheaper quantity : Dearer quantity) = (Dearer price - Mean price) : (Mean price - Cheaper price)

In this case, the "price" is the fraction of spirit in the mixture.

So,

(Quantity of mixture from Vessel A : Quantity of mixture from Vessel B) = (Fraction of spirit in Vessel B - Fraction of spirit in Vessel C) : (Fraction of spirit in Vessel C - Fraction of spirit in Vessel A)

Substituting the values, we get:

(Quantity of mixture from Vessel A : Quantity of mixture from Vessel B) = (7/13 - 8/13) : (8/13 - 5/7)

Solving this, we get:

(Quantity of mixture from Vessel A : Quantity of mixture from Vessel B) = (-1/13) : (9/91)

Since the ratio cannot be negative, we take the absolute values, which gives us:

(Quantity of mixture from Vessel A : Quantity of mixture from Vessel B) = 1/13 : 9/91

Solving this further, we get:

(Quantity of mixture from Vessel A : Quantity of mixture from Vessel B) = 7 : 9

So, the mixtures from Vessel A and Vessel B should be mixed in the ratio 7:9 to obtain a new mixture in Vessel C containing spirit and water in the ratio 8:5. Therefore, the answer is 7:9.

To solve this problem, we need to use the rule of alligation which is a rule that allows us to find the ratio in which two or more ingredients at a given price must be mixed to produce a mixture of a desired price.

Step 1: Calculate the fraction of spirit in each vessel

Vessel A: The ratio of spirit to water is 5:2, so the fraction of spirit is 5/(5+2) = 5/7

Vessel B: The ratio of spirit to water is 7:6, so the fraction of spirit is 7/(7+6) = 7/13

Vessel C: The ratio of spirit to water is 8:5, so the fraction of spirit is 8/(8+5) = 8/13

Step 2: Use the rule of alligation

The rule of alligation states that:

(Cheap quantity : Dear quantity) = (Cost of dear - Mean price) : (Mean price - Cost of cheap)

In this case, the "cheap" quantity is the mixture from Vessel A (because it has a lower fraction of spirit) and the "dear" quantity is the mixture from Vessel B.

So, we have:

(Cheap quantity : Dear quantity) = (7/13 - 8/13) : (8/13 - 5/7)

Solving this gives us:

(Cheap quantity : Dear quantity) = (-1/13) : (1/91)

Since we can't have a negative quantity, we take the absolute value to get:

(Cheap quantity : Dear quantity) = (1/13) : (1/91)

Simplifying this ratio gives us:

(Cheap quantity : Dear quantity) = 7 : 1

So, the mixtures from Vessels A and B should be mixed in the ratio 7:1 to obtain a new mixture in Vessel C containing spirit and water in the ratio 8:5.

This problem can be solved using the rule of alligation. The rule of alligation allows us to find the ratio in which two or more ingredients at the given price must be mixed to produce a mixture of a desired price.

Step 1: Calculate the fraction of spirit in each vessel

Vessel A: 5/(5+2) = 5/7 Vessel B: 7/(7+6) = 7/13

Step 2: Calculate the fraction of spirit in the final mixture

Vessel C: 8/(8+5) = 8/13

Step 3: Use the rule of alligation

The rule of alligation states that:

(Cheaper quantity) : (Dearer quantity) = (Dearer price - Mean price) : (Mean price - Cheaper price)

In this case, the "cheaper" mixture is the one with the lower fraction of spirit (Vessel A), and the "dearer" mixture is the one with the higher fraction of spirit (Vessel B).

So, we have:

(Vessel A quantity) : (Vessel B quantity) = (7/13 - 8/13) : (8/13 - 5/7)

Solving this gives us:

(Vessel A quantity) : (Vessel B quantity) = 1/13 : 9/91

Simplifying this ratio gives us:

(Vessel A quantity) : (Vessel B quantity) = 7 : 1

So, the mixtures in Vessels A and B should be mixed in the ratio 7:1 to obtain a mixture in Vessel C with spirit and water in the ratio 8:5.