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Q.

The fuel indicator in a car shows one-fifth of the fuel tank as full. When 22 more liters 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 ( $in liters$ ) is

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a

10 liters

b

12 liters

c

5 liters

d

8 liters

answer is D.

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Detailed Solution

Concept- We need to discover the preliminary gas stage. The overall gas potential of the tank would be 5 instances of the preliminary gas content material in the tank. here, will equate the fashioned equation from the above question in phrases of gas amount. in which, we can expect the initial gasoline amount as a variable quantity & will shape a linear equation in a single variable.
Let’s breakdown the math here:

x = \frac{1}{5} (tank capacity)

.
Thereby, tank capacity is equal to

5 x

.After adding 22 more liters to

x

, fuel level is

\frac{3}{4} th

of full tank capacity. So,

x + 22 = \frac{3}{4} (tank capacity)

So, the above equation becomes

x + 22 = \frac{3}{4} \times (5 x)

\Rightarrow x + 22 = \frac{1}{5} \times 4

\Rightarrow 22 = \frac{1}{5} \times 4 - x

\Rightarrow \frac{1}{5} \times 4 - x = 22

\Rightarrow \frac{(15 x - 4 x)}{4} = 22

\Rightarrow \frac{11 x}{4} = 22

\Rightarrow 11 x = 88

\Rightarrow x = 8

Hence, the correct option is 4) 8 liters

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