## Wednesday, 23 November 2011

### Arithmetic-21 (IIFT-2009)

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 follows here:
Solution:
For calculating the quantity of petrol removed in each interaction, we need to consider proportion of petrol in the petrol-kerosene 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 petrol-kerosene 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 interaction-II is nothing but 1/10th of the “Remaining petrol” of its previous interaction ie., interaction-I. Similarly, “Removed petrol” in the interaction-III is nothing but 1/10th of the “Remaining petrol” of its previous interaction ie., interaction-II. 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 = 36 360-36 = 324 III 40*(324/400) = 324/10 = 32.4 324-32.4 = 291.6 IV 29.16 291.6-29.16 = 262.44 V 26.244 262.44-26.244 = 236.196 VI 23.6196 236.196-23.6196 = 212.5764 VII 21.25764

Finally we get the “Petrol quantity” received by 7th customer is 21.25764 litres