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Question
Car A travels x km for every litre of petrol, while car B travels (x + 5) km for every litre of petrol.
If car A use 4 litre of petrol more than car B in covering the 400 km, write down and equation in x and solve it to determine the number of litre of petrol used by car B for the journey.
Solution
Given Distance = 400 km
Car A travels x km/litre.
Car B travels (x + 5) km/litre.
Car A uses 4 litre more than car B
∴ `(400)/x - (400)/(x + 5)` = 4
400 (x + 5) - 400x = 4x(x + 5)
400x + 2000 - 400x = 4x2 + 20x
4x2 + 20x - 200 = 0
4 (x2 + 5x - 500) = 0
x2 + 25x - 20x - 500 = 0
x (x + 25) - 20 (x + 25) = 0
(x + 25) (x - 20) = 0
∴ x = 20 - 25 ...(inadmissible)
No. of litre of petrol used by car B
= `(400)/(20 + 5)`
= `(800)/(25)`
= 16.
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