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Three bags whose volumes are in the ratio of 3 : 5 : 7 are full of lime and silica. In the 1st bag the ratio of lime and silica is 5 : 1, in 2nd bag the ratio is 7 : 3 and in the 3rd bag the ratio is 3 : 4. All the three mixtures are mixed in another bag. Find the ratio of lime and silica in the final mixture.

Three bags whose volumes are in the ratio of 3 : 5 : 7 are full of lime and silica. In the 1st bag the ratio of lime and silica is 5 : 1, in 2nd bag the ratio is 7 : 3 and in the 3rd bag the ratio is 3 : 4. All the three mixtures are mixed in another bag. Find the ratio of lime and silica in the final mixture. Correct Answer 3 : 2

Given:

Ratio of volumes of 3 bags = 3 : 5 : 7

Ratio of Lime and Silica in 1st bag = 5 : 1

Ratio of Lime and Silica in 2nd bag = 7 : 3

Ratio of Lime and Silica in 3rd bag = 3 : 4

Concept used:

Total quantity of Lime in final bag = Lime in 1st bag + Lime in 2nd bag + Lime in 3rd bag

& Total quantity of Silica in final bag = Silica in 1st bag + Silica in 2nd bag + Silica in 3rd bag

Calculation:

In 1st bag of 3 litres

Quantity of Lime = 3 × 5 / 6 = 5 / 2 litres

Quantity of Silica = 3 × 1 / 6 = 1 / 2 litres

In 2nd bag of 5 litres

Quantity of Lime = 5 × 7 / 10 = 5 / 2 litres

Quantity of Silica = 5 × 3 / 10 = 3 / 2 litres

In 3rd bag of 7 litres

Quantity of Lime = 7 × 3 / 7 = 3 litres

Quantity of Silica = 7 × 4 / 7 = 4 litres

Now, Total quantity of Lime in 3 bags = (5 / 2 + 7 / 2 + 3)

⇒ Total quantity of Lime in 3 bags = 9 litres

Total quantity of Silica in 3 bags = (1 / 2 + 3 / 2 + 4)

⇒ Total quantity of Silica in 3 bags = 6 litres

Now, Ratio of Lime and Silica in the final mixture = 9 : 6

⇒ Ratio of Lime and Silica in the final mixture = 3 : 2

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