Question

A tank full of petrol. if 12 lit petrol is taken out and replaced by kerosene, again 12 lit. mixture is taken out and replaced by kerosene and this process continues one more time in the same manner at the end the ratio of petrol to kerosene is 27: 1701. find the initial quantity of petrol?

Answer 1

quantity of petrol of petrol is 12-6=6

Answer 2

If at the end the ratio of petrol to kerosene is 27: 1701, then the initial quantity of petrol is 16 litres.

Step-by-step explanation:

Let the initial quantity of petrol in the yank be “x” units.

It is given that,

The quantity of petrol taken out and replaced by the same quantity of kerosene = 12 litres  

No. of repetition of the process, n = 3

The final ratio of petrol to kerosene after the “n = 3” operations = 27:1701

We know that the formula for finding the quantity of pure liquid after n operations is given by = x[1 – ($\frac{y}{x}$)]ⁿ units

Therefore,  

The equation for the ratio of petrol to mixture after n operations is given by,

$x\frac{(1 - \frac{12}{x})^3}{x}$ = $\frac{27}{1701 + 27}$

⇒ $x\frac{(1 - \frac{12}{x} )^3}{x} = \frac{27}{1728}$

⇒ {1 – ($\frac{12}{x}$)}³ = $\frac{27}{1728}$

taking cube roots on both sides

⇒ {1 – ($\frac{12}{x}$)} = $\frac{3}{12}$

⇒ 12(x – 12) = 3x

⇒ 12x – 144 = 3x

⇒ 9x = 144

⇒ x = 16

Thus, the initial quantity of petrol is 16 litres.

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