The average of $15$ results is $50$ . If the average of first $8$ results is $48$ and that of the last $8$ is $53$ , find the eigth result.

95

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80

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71

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58

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Solution

The correct option is D $58$
Let $r_{1}, r_{2}, r_{3}, . . ., r_{15}$ be the 15 results.
$According to given question$
$\frac{r_{1} + r_{2} + r_{3} + . . . + r_{15}}{15} = 50$
$\Rightarrow r_{1} + r_{2} + r_{3} + . . . + r_{15} = 50 \times 15$
$\Rightarrow r_{1} + r_{2} + r_{3} + . . . + r_{15} = 750$ $. . . (i)$
$A g a i n, \frac{r_{1} + r_{2} + r_{3} + . . . + r_{8}}{8} = 48$
$\Rightarrow r_{1} + r_{2} + r_{3} + . . . + r_{8} = 384$ $. . . (i i)$
$A l s o, \frac{r_{8} + r_{9} + r_{10} + . . . + r_{15}}{8} = 53$
$r_{8} + r_{9} + r_{10} + . . . + r_{15} = 424$ $. . . (i i i)$
$On adding (ii) and (iii), we get$
$r_{1} + r_{2} + r_{3} + . . . + r_{15} + r_{8} = 384 + 424$
$\Rightarrow r_{8} = 384 + 424 - 750 = 58$ (from (i))

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