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In four vessels each of 20 liters capacity, in which mixture of water and honey is filled. The ratios of water and honey are 3 : 2, 2 : 1, 5 : 3, and 4 : 3 in the four respective vessels. If all the vessels are emptied into a single large vessel, find the proportion of water and honey in the mixture.

In four vessels each of 20 liters capacity, in which mixture of water and honey is filled. The ratios of water and honey are 3 : 2, 2 : 1, 5 : 3, and 4 : 3 in the four respective vessels. If all the vessels are emptied into a single large vessel, find the proportion of water and honey in the mixture. Correct Answer 2069 : 1291

Given:

Ratio of water to honey in first vessel = 3 : 2

Ratio of water to honey in second vessel = 2 : 1

Ratio of water to honey in third vessel = 5 : 3

Ratio of water to honey in fourth vessel = 4 : 3

Concept used:

Ratio of water to honey in final mixture = (Quantity of water in first vessel + Quantity of water in second vessel + Quantity of water in third vessel + Quantity of water in fourth vessel) : (Quantity of honey in first vessel + Quantity of honey in second vessel + Quantity of honey in third vessel + Quantity of honey in fourth vessel)                    

Calculation:

Quantity of water in first vessel = {20 × (3/5)}

⇒ 12 liters

Quantity of water in second vessel = {20 × (2/3)}

⇒ 40/3 liters

Quantity of water in third vessel = {20 × (5/8)}

⇒ 25/2 liters

Quantity of water in fourth vessel = {20 × (4/7)}

⇒ 80/7 liters

Quantity of honey in first vessel = {20 × (2/5)}

⇒ 8 liters

Quantity of honey in second vessel = {20 × (1/3)}

⇒ 20/3 liters

Quantity of honey in third vessel = {20 × (3/8)}

⇒ 15/2 liters

Quantity of honey in fourth vessel = {20 × (3/7)}

⇒ 60/7 liters

Ratio of water to honey in final mixture = {(12) + (40/3) + (25/2) + (80/7)} : {(8) + (20/3) + (15/2) + (60/7)}

⇒ {(504 + 560 + 525 + 480)/42} : {(336 + 280 + 315 + 360)/42}

⇒ 2069 : 1291

∴ The ratio of water to honey in the final mixture is 2069 : 1291.

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