A) 10 yr 4 months
B) 12 yr 4 months
C) 13 yr 6 months
D) 11 yr 2 months
Correct Answer: A
Solution :
| [a] Total age of 30 students \[=30\times \left( 14+\frac{4}{12} \right)=30\times \left( 14+\frac{1}{3} \right)\] \[=10\times 43=430\,\,yr\] Total age of 35 students \[=35\times \left( 13+\frac{9}{12} \right)=35\times \left( 13+\frac{3}{4} \right)\] \[=\frac{35\times 55}{4}yr\] \[\therefore \] The age of youngest student out of 5 new students is 9 yr 11 months i.e., \[\frac{119}{12}yr,\] \[\therefore \] The average age of remaining 4 new students \[=\frac{\frac{35\times 55}{4}-430-\frac{119}{12}}{4}\] \[=\frac{3\times 35\times 55-430\times 12-119}{12\times 4}\] \[=\frac{5775-5160-119}{12\times 4}\] \[=\frac{5775-5279}{12\times 4}\] \[=\frac{496}{12\times 4}\] \[=\frac{124}{12}=10\,\,yr4\,\,\text{month}\] |
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