Problem Solving

At the end of the year, the six members of the board of directors of a large computer company each receive a different number of the twelve shares of an executive bonus package. The total amount of the bonus is equal to the average of 1.5% of the company's net profit and 5 times the number of computers sold. If the Chief Technology Officer receives 2 shares of the bonus and was paid $1.65 million in bonus money at the end of a year when the company sold 2.6 million computers, what was the company's net profit for that year?

$6.8 million

$453 million

$906 million

$1,147 million

$2,293 million



b

average of two things is to be taken :
so let net profit = X

u will get this equation

1.6* 10^6= [(1.5X/100 + 5*2.6*10^6)/24 ] *2

solve for X u will get X as 453 million

The total amount of the bonus is equal to the average of 1.5% of the company's net profit and 5 times the number of computers sold

once u have total amount then this total amount of bonus will be shared in 12 shares so get the amt of bonus for 2 shares .this amt of bonus for 2 shares is what this one member got in terms of money (in a company money is equivalent to shares !! )equal to 1.65 million

bonus = average of 1.5% of net profit and 5 times sales.

total bonus is divided in 12 parts. out of which chief technology officer received 2 parts for 1.65 million. So the total bonus must be 9.9 millions.

so 9.9 = (1.5%of N + 5S)/2 ----> 19.8=1.5% of N + 13 ------> 6.8=1.5% of N ------> 6.8=(1.5/100)N ------------> 680/1.5 = 453.33 = N

Regards,

Abhijit

varun289 wrote:At the end of the year, the six members of the board of directors of a large computer company each receive a different number of the twelve shares of an executive bonus package. The total amount of the bonus is equal to the average of 1.5% of the company's net profit and 5 times the number of computers sold. If the Chief Technology Officer receives 2 shares of the bonus and was paid $1.65 million in bonus money at the end of a year when the company sold 2.6 million computers, what was the company's net profit for that year?

$6.8 million

$453 million

$906 million

$1,147 million

$2,293 million

To avoid tedious math, BALLPARK and use the answer choices, which represent the net profit.

CTO's shares/total shares = 2/12 = 1/6.
Thus, the 1.65 million received by the CTO is equal to 1/6 of the total bonus:
1.65 = (1/6)T.
T = 6(1.65) ≈ 10 million.

Since 2.6 million computers were sold, 5 times the number of computers = 5(2.6) = 13 million.

Since the bonus of 10 million is the AVERAGE of 13 million and 1.5% of the net profit, 10 million must be HALFWAY between 13 million and 1.5% of the net profit.
Thus, 1.5% of the correct answer choice must yield a value around 7 million.
Since (.015)(400) = 6 million, the only viable answer choice is 453 million.

The correct answer is B.