Question
In a tank, the ratio of petrol to kerosene is 7:5. 50% of
this mixture is removed and replaced with kerosene. Again, 50% is replaced with petrol. Find the final ratio of petrol to kerosene in the tank.Solution
ATQ,
Petrol = 7x, Kerosene = 5x → Total = 12x litres
First step (50% replaced with kerosene):
Petrol = 0.5 × 7x = 3.5x litres
Kerosene = 0.5 × 5x + 0.5 × 12x = 2.5x + 6x = 8.5x litres
Second step (50% replaced with petrol):
Petrol = 0.5 × 3.5x + 0.5 × 12x = 1.75x + 6x = 7.75x litres
Kerosene = 0.5 × 8.5x = 4.25x litres
Final ratio = 7.75x : 4.25x = 775 : 425 = 31:17
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