Question

The fuel indicator in a car shows one-fifth of the fuel tank as full. When 22 more litres of fuel are poured into a tank, the indicator rests at the three-fourth of the full mark. Then, the amount of the fuel in the fuel tank at starting (in litres) is

Answer 1

Hint: Need to find out the initial fuel level. The total fuel capacity of the tank would be 5 times the initial fuel content in the tank. Here, will equate the formed equation from the above question in terms of fuel amount. Where, we will assume initial fuel amount as a variable quantity & will form a linear equation in one variable.
Complete step by step solution:
Let’s breakdown the math here:
Let's say the initial fuel level is X litres. X is one-fifth of Full tank capacity i.e. X = 1/5(tank capacity).
Thereby, tank capacity is equal to 5X. So, we will have to figure out what's X.
After adding 22 more litres to X, fuel level is 3/4 th of full tank capacity. So,
X+22 = 3/4(tank capacity)
We have previously established that tank capacity is 5X. So, the above equation becomes
\[\begin{align}
  & X+22=\dfrac{3}{4}\times \left( 5X \right) \\
 & \Rightarrow X+22=\dfrac{15X}{4} \\
 & \Rightarrow 22=\dfrac{15X}{4}-X \\
 & \Rightarrow \dfrac{15X}{4}-X=22 \\
 & \Rightarrow \dfrac{\left( 15X-4X \right)}{4}=22 \\
 & \Rightarrow \dfrac{11X}{4}=22 \\
 & \Rightarrow 11X=88 \\
 & \Rightarrow X=8 \\
\end{align}\]
Therefore, the amount of fuel starting in the fuel tank is 8 Litres.

Note: Here, be careful, no need to divide by 5 the value of X found to find initial fuel amount in fuel tank. Because we assumed X as the initial fuel capacity, not the whole fuel capacity of the tank. In the question, if it was asked to find the full capacity of the fuel tank, Then, we had to multiply by 5 in X to get the full capacity of the fuel tank.