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Mathematics

Two cars X and Y use 1 litre of diesel to travel x km and (x + 3) km respectively. If both the cars covered a distance of 72 km, then :

The amount of diesel used by car X is:

  1. 6 litres

  2. 12 litres

  3. 18 litres

  4. 24 litres

Quadratic Equations

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Answer

Solving,

⇒72x−72x+3=4⇒72(x+3)−72xx(x+3)=4⇒72x+216−72xx2+3x=4⇒216=4(x2+3x)⇒2164=(x2+3x)⇒54=(x2+3x)⇒x2+3x−54=0⇒x2+9x−6x−54=0⇒x(x+9)−6(x+9)=0⇒(x−6)(x+9)=0⇒(x−6)=0 or (x+9)=0….[Using zero-product rule]⇒x=6 or x=−9.\Rightarrow \dfrac{72}{x} - \dfrac{72}{x + 3} = 4 \\[1em] \Rightarrow \dfrac{72(x + 3) - 72x}{x(x + 3)} = 4 \\[1em] \Rightarrow \dfrac{72x + 216 - 72x}{x^2 + 3x} = 4 \\[1em] \Rightarrow 216 = 4(x^2 + 3x) \\[1em] \Rightarrow \dfrac{216}{4} = (x^2 + 3x) \\[1em] \Rightarrow 54 = (x^2 + 3x) \\[1em] \Rightarrow x^2 + 3x - 54 = 0 \\[1em] \Rightarrow x^2 + 9x - 6x - 54 = 0 \\[1em] \Rightarrow x(x + 9) - 6(x + 9) = 0 \\[1em] \Rightarrow (x - 6)(x + 9) = 0 \\[1em] \Rightarrow (x - 6) = 0 \text{ or } (x + 9) = 0 \text{….[Using zero-product rule]}\\[1em] \Rightarrow x = 6 \text{ or } x = -9.

Distance covered cannot be negative.

Thus, x = 6.

Diesel used by car X = 72x\dfrac{72}{x}

= 726\dfrac{72}{6}

= 12 litres.

Hence, option 2 is the correct option.

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