### Question 7

SSC-CGL 2020 Mar 4 Shift 2

The average weight of N persons is 56.5 kg. When 5 more persons join, the average increases by 0.55 kg. If the average of 5 new members is 64.2 kg, then N is?

### Solution in Detail

Average of N given $\displaystyle 56.5$

$\displaystyle \therefore $ total weight is $\displaystyle 56.5 \times N$

Average of new $\displaystyle 5$ given = $\displaystyle 64.2$

$\displaystyle \therefore $ weight $\displaystyle = 5 \times 64.2 = 321$

New avg. $\displaystyle = \frac{56.5N + 321}{N + 5}\text{. . . (1)}$

It is given that average after 5 new are added increases by 0.55 kg. So the new average already given as $\displaystyle 56.5 + 0.55 = 57.05$ kg. Equating to (1)

$\displaystyle \therefore 57.05 = \frac{56.5N + 321}{N + 5}$

Solving, $\displaystyle N = 65\:\underline{Ans}$

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