Question

There are M employees working in a factory. The $n^{th}$ employee does n units of work each day for n days, where n = 1 to M. The total amount of work completed by them is 385 units in M days. Find the number of employees working in the factory.

• A. 10
• B. 11
• C. 13
• D. 15
• E. None of these

Answer 1

The correct option is A 10

It is given that $n^{th}$ employee does n units of work each day for n days,
$\Rightarrow$ $1^{st}$ employee does 1 unit of work for 1 day. Total work done by $1^{st}$ employee is $1^{\ast }1$ = 1
$\Rightarrow$ $2^{nd}$ employee does 2 unit of work each day for 2 days. Total work done by $2^{nd}$ employee is $2^{\ast }2$ = 4
$\Rightarrow$ Total work done by $M^{th}$employee = $m^{\ast }m=m^2$
$\Rightarrow$ So the total work done is $1^2+2^2+3^2...m^2=385$
$\Sigma m^2=\frac{\left(m\right)(m+1)(2m+1)}{6}=385.$ On solving we get m = 10