| A petrol tank at a filling station has a capacity of 400 L. The attendant sells 40 L 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 L of petrol? [FCI (Assistant) Grade III 2015] |
A) 21.25 L
B) 20.25 L
C) 23.25 L
D) 24.25 L
Correct Answer: A
Solution :
| Here, \[n=6,\] \[x=400\,L,\]\[y=40\,L\] |
| \[\therefore \] Quantity of pure petrol in tank \[=x\,{{\left( 1-\frac{y}{x} \right)}^{n}}\] |
| \[=400{{\left( 1-\frac{40}{400} \right)}^{6}}=400{{\left( 1-\frac{1}{10} \right)}^{6}}\] |
| \[=400\times {{\left( \frac{9}{10} \right)}^{6}}\] |
| \[=\,\,400\times \frac{9}{10}\times \frac{9}{10}\times \frac{9}{10}\times \frac{9}{10}\times \frac{9}{10}\times \frac{9}{10}\] |
| \[=\,\,4\times 81\times \frac{81}{100}\times \frac{81}{100}\] |
| \[=\,\,\frac{81\times 81\times 81}{2500}\] |
| \[=\,\,\frac{531441}{2500}=212.57\,\,L\] |
| Now, quantity of pure petrol get by seventh customer, if he purchases 40 L of petrol |
| \[=212.57\times \frac{40}{400}\,=\,\,21.257=21.25\,L\] |
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