An empty fuel tank of a car was filled with A type petrol. When the tank was half-empty, it was filled with B type petrol. Again when the tank was half-empty, it was filled with A type petrol. When the tank was half-empty again, it was filled with B type petrol. What is the percentage of A type petrol at present in the tank ?
A. 37.5%
B. 35.5%
C. 30%
D. 60%
Answer: Option A
Solution(By Examveda Team)
Let the capacity of the tank be 100 litres.Then,
Initially :
A type petrol = 100 litres
After first operation :
A type petrol = $$\left( {\frac{{100}}{{2}}} \right)$$ = 50 litres ;
B type petrol = 50 litres
After second operation :
A type petrol = $$\left( {\frac{{50}}{2} + 50} \right)$$ = 75 litres
B type petrol = $$\left( {\frac{{50}}{2}} \right)$$ = 25 litres
After third operation :
A type petrol = $$\left( {\frac{{75}}{2}} \right)$$ = 37.5 litres
B type petrol = $$\left( {\frac{{25}}{2} + 50} \right)$$ = 62.5 litres
∴ Required percentage = 37.5%
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Related Questions on Percentage
A. $$\frac{1}{4}$$
B. $$\frac{1}{3}$$
C. $$\frac{1}{2}$$
D. $$\frac{2}{3}$$
Let capacity of full tank x
X= a(filled with a-typ petrol)
After 1st operation
X=a/2+b/2
After 2nd operation
X=(a/2+b/2)/2 + a/2
After 3rd operation
X={(a/2+ b/2)/2}/2 + b/2
After solving
X=3/8a + 5/8b
So remaining a-typ petrol=3/8 ×100 =37.5%