Question 5
SSC-CGL 2020 Mar 3 Shift 1
The average of first 5 numbers out of 6 numbers is equal to 7 times the 6-th number. If average of all the numbers is 138, then what is the 6-th number?
Solution in Short
Let 6-th number be = X. By the concept of averages, each of the first five numbers can be levelled at their given average = 7X. Average of all the six numbers is (5 x 7X + X)/6 = 6X = 138 (given), from where we get X = 23 ans!
Solution in Detail
Let the sixth number = $\displaystyle x$
Average of first five given = 7x
$\displaystyle \implies \frac{\text{ sum of first five}}{5} = 7x$
$\displaystyle \implies \text{ sum of first five} = 35x$
Average of all the six = $\displaystyle \frac{\text{sum of all}}{6}$
$\displaystyle = \frac{35x + x}{6} = 138 \text{(given)}$
$\displaystyle \implies 6x = 138 \implies x = 23\:\text{Ans}$
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