Question

answer this question​

Answer 1

Given : Eight members of the club donated Rs. 100 each

$:\implies$  Total Amount donated by Eight members = Rs. (100 × 8)

$:\implies$  Total Amount donated by Eight members = Rs. 800

Given : President donates Rs. 50 more than the average donation of all (including President) of them.

Let the Amount donated by the President be : P

$\bigstar\;\;\textsf{We know that : \boxed{\mathsf{Average = \dfrac{Sum\;of\;all\;the\;Observations}{Total\;Number\;of\;Observations}}}}$

$\bigstar\;\;\mathsf{Average\;Donation = \dfrac{8\;Members\;Donation + President\;Donation}{Total\;Number\;of\;Members\;(including\;President)}}$

$\implies \mathsf{Average\;Donation = \dfrac{800 + P}{8 + 1}}$

$\implies \mathsf{Average\;Donation = \dfrac{800 + P}{9}}$

As the President donated Rs. 50 more than Average donation :

$\mathsf{\implies \dfrac{800 + P}{9} + 50 = P}$

$\mathsf{\implies \dfrac{800 + P + 50(9)}{9} = P}$

$\mathsf{\implies \dfrac{800 + P + 450}{9} = P}$

$\mathsf{\implies \dfrac{P + 1250}{9} = P}$

$\mathsf{\implies P + 1250 = 9P}$

$\mathsf{\implies 9P - P = 1250}$

$\mathsf{\implies 8P = 1250}$

$\mathsf{\implies P = \dfrac{1250}{8}}$

$\mathsf{\implies P = 156.25}$

Answer : Contribution of President is Rs. 156.25