Average age of 15 students of a class is 15, years. Out of these average age of 5 students is 14 ,ye

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Average age of $15$ students of a class is $15\, years.$ Out of these the average age of $5$ students is $14 \,years$ and that of the other $9$ students is $16\, years.$ The age of the $15^{th}$ student is (in $years$)

A

$11$

B

$14$

C

$15$

D

$15 \frac{2}{7}$

Solution

Total age of $15$ students $=15 \times 15=225$ years…..$(1)$

Sum of ages of $5$ students $=5 \times 14=70$ years…..$(2)$

Sum of ages of $9$ students $=9 \times 16=144$ years…..$(3)$

$\therefore$ Age of $15^{th}$ student $=(1)-(2)-(3)=225-(70+144)=11$ years

Standard 13

Quantitative Aptitude

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