| The average age of 45 persons is decreased by \[\frac{1}{9}yr,\]when one of them having \[60\,\,yr\]is replaced by a new comer. Then, the age of the new comer is |
A) \[45\,\,yr\]
B) \[55\,\,yr\]
C) \[59\,\,yr\]
D) \[49\,\,yr\]
Correct Answer: B
Solution :
| Let the average age of 45 persons \[=x\] |
| Then, sum of the ages \[=45x\] |
| According to the question, |
| \[\frac{45x+\text{(Age}\,\,\text{of}\,\,\text{new}\,\,\text{person)}-60}{45}=x-\frac{1}{9}\] |
| \[\Rightarrow \]\[45x+\](Age of new person) \[-\,60=45\left( x-\frac{1}{9} \right)\] |
| Age of new person \[-\,\,60=-\,\,5\] |
| \[\Rightarrow \]Age of new person \[=55\,\,yr\] |
| Alternate Method |
| Age of new person \[=(a-nb)\] |
| where, \[a=60,\]\[n=45,\]\[b=\frac{1}{9}\] |
| \[\therefore \]Age of the new person \[=60-45\times \frac{1}{9}=55\,\,yr\] |
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