The average age of 10 children is 8 years 2 months.If the average age of 9 children is 6 years 2 months, find the age of the 10th child.

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Solution

Dear Student,

$A v e r a g e a g e o f 10 c h i l d r e n s = 8 y e a r s 2 m o n t h s = 8 \times 12 + 2 = 98 m o n t h s S o t o t a l a g e o f 10 c h i l d r e n s = 10 \times 98 = 980 m o n t h s A v e r a g e a r e o f 9 c h i l d r e n s = 6 y e a r s 2 m o n t h = 6 \times 12 + 2 = 74 m o n t h s S o t o t a l a g e o f 9 c h i l d e n s = 9 \times 74 = 666 m o n t h s T h e r e f o r e a g e o f 10^{t h} c h i l d = t o t a l a g e o f 10 c h i l d r e n - t o t a l a g e o f 9 c h i l d r e n = 980 - 666 = 314 = 26 y e a r s 2 m o n t h s$
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