### 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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