A petrol tank at a filling station has a capacity of 400
litres. The attendant sells 40 litres of petrol from the tank to one customer
and then replenishes it with kerosene oil. This process is repeated with six
customers. What quantity of pure petrol will the seventh customer get when he
purchases 40 litres of petrol?
A. 20.50 litres B. 21.25 litres C. 24.75 litres D. 22.40 litres
Solution:
A. 20.50 litres B. 21.25 litres C. 24.75 litres D. 22.40 litres
Solution follows here:
For calculating the quantity of petrol
removed in each interaction, we need to consider proportion of petrol in the
petrolkerosene mixture of the previous interaction. For example, in the first
interaction 40 litres of petrol is removed and 40 litres of Kerosene is added.
This leaves 360 litres of petrol and 40 litres of kerosene in the resulting
mixture. In the second interaction when 40 litres of the liquid is taken out,
it is not pure petrol. Pure petrol is to be calculated from the petrolkerosene
proportion of 360:40. This makes the calculation a bit intensive when we go
from one interaction to another. But there is a pattern
to be followed to make it simple:
Observe the following table, where in, “Removed
petrol” and “Remaining petrol” are calculated for each interaction. The point
here is “Removed petrol” in the interactionII is nothing but 1/10^{th}
of the “Remaining petrol” of its previous interaction ie., interactionI.
Similarly, “Removed petrol” in the interactionIII is nothing but 1/10^{th}
of the “Remaining petrol” of its previous interaction ie., interactionII. This
pattern can be followed in the next interactions to make the calculation much
simpler.
customer

Removed Petrol

Remaining Petrol

I

40

360

II

40*(360/400) = 360/10 = 36

36036 = 324

III

40*(324/400) = 324/10 = 32.4

32432.4 = 291.6

IV

29.16

291.629.16 = 262.44

V

26.244

262.4426.244 = 236.196

VI

23.6196

236.19623.6196 = 212.5764

VII

21.25764

Finally we get the “Petrol quantity” received by 7^{th}
customer is 21.25764
litres
Nearest answer option is ‘B’
Answer (B)
Thanks you for the detailing
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