| A container contains 60 L of milk. From this container \[\frac{1}{10}\]of milk was taken out and was replaced by water. This process is repeated further two times. The amount of milk left in the container is [SSC (10+2) 2012] |
A) 34.24 kg
B) 39.64 kg
C) 43.74 kg
D) 47.60 kg
Correct Answer: C
Solution :
| Given, pure milk in container\[=60\,\,L\] |
| By replacing\[\frac{1}{10}\]part by water, |
| Remaining milk \[=60-\frac{1}{10}\times 60=54\,\,L\] |
| Again, replacing\[\frac{1}{10}\] part by water, |
| Remaining-milk \[=54-\frac{1}{10}\times 54=48.6\,\,L\] |
| Again, replacing \[\frac{1}{10}\]part by water, |
| Remaining milk \[=48.6-\frac{1}{10}\times 48.6=43.74\,\,L\] |
| Alternate Method |
| Given, \[x=60\,\,L,\]\[n=3,\]\[a=6\] |
| Amount of milk left \[=x{{\left( 1-\frac{a}{x} \right)}^{n}}\] |
| \[=60{{\left( 1-\frac{6}{60} \right)}^{3}}=43.74\,\,L\] |
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