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A solution contains petrol and kerosene in the ratio of 3 ∶ 5. 16 liters of the solution has been replaced with petrol to create a ratio of 5 ∶ 3. Find the original amount of kerosene in the solution.
1. 40 liters
2. 35 liters
3. 30 liters
4. 25 liters

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Correct Answer - Option 4 : 25 liters

Given:

The ratio of petrol to kerosene = 3 : 5

Quantity of solution replaced with petrol = 16 litres

New ratio of petrol to kerosene = 5 : 3

Calculation:

Let the initial quantity of petrol and kerosene be 3x and 5x  

16 litres of solution replaced with petrol

The solution also in the ratio 3 : 5 

so petrol in the replaced solution = (3/8) × 16 = 6 litres 

Kerosene in the replaced solution = (5/8) × 16 = 10 litres  

According to the question

⇒ (3x - 6 + 16)/(5x - 10) = 5/3      

⇒ (3x + 10)/(5x - 10) = 5/3

⇒ 3(3x + 10) = 5(5x - 10)

⇒ 9x + 30 = 25x - 50 

⇒16x = 80

⇒ x = 5

The original amount of kerosene = 5x = 25 litres

∴ The original amount of kerosene in the solution is 25 litres

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