Please SHOW the MATH In a certain company 30 percent of the

Please SHOW the MATH!

In a certain company, 30 percent of the men and 20 percent of the women attend night school. If 40 percent of all employees are men, what percent of all the employees attend night school?

a. 15                       b. 24                             c. 35                 d. 44                             e. none

The length of the shadow of a flagpole was found to be 72 feet. The shadow of a 3 foot picket fence in line with the flagpole was 4 feet. What is the height of the flagpole?

a. 54 feet                b. 63 feet                      c. 27 feet          d. 84 feet                      e. none

3.      The sum of both digits, of either of two two-digit numbers, in whatever order the digits are written, is 9. The square of either of the digits of either number, minus the product of both digits, plus the square of the other digit is the number 21. The numbers are _______?

a. 36, 63                 b. 81, 18                       c. 27, 72           d. 45, 54                       e. none

4.      If a boat goes downstream 72 miles in 3 hours and upstream 60 miles in 6 hours, the rate of the river and the rate of the boat in still water respectively are ________?

a. 7 & 16 mph        b. 7 & 17 mph              c. 6 & 17 mph d. 6 & 18 mph              e. none

5.      Three times the square of a certain positive number exceeds six times the number by nine. Find the number:

a. 3                         b. 6                              c. 4                   d. 9                              e. none

6.      The width of a rectangle is 15 feet less than its length, and the perimeter is 210 feet. Find the width:

a. 60 feet                b. 35 feet                      c. 45 feet          d. 40 feet                      e. none

7.      If 6 men can do a piece of work in 14 days, how many men are needed to do the work in 21 days?

a. 3                         b. 9                              c. 5                   d. 4                              e. none

The sum of two numbers is 17 and the sum of their square is 145. Find the larger number.

a. 10                       b. 11                 c. 8                               d. 9                              e. none

9.      A certain sum of money is invested at 10%. Twice that amount is invested at 8%. The total amount of interest from both investments is $91. How much is invested at 8%?

a. $350                   b. $500             c. $1000                       d. $700                         e. none

10.   A mother left 20% of her estate to one son and 25% to another son. The remaining $55,000 she left to her daughter. Find the amount of the estate:

a. $90,000               b. $100,000       c. $110,000                   d. $120,000                   e. none

Solution

2. 40% of all employees are men.

   out of which 30% attend night school i.e 0.3 x 0.4 = 0.12 = 12%

now 60% of all employees are women out of which 20% women attend night school.

so, % of women attending night school out of all employees = 0.2 x 0.6 = 0.12 = 12%

therefore total % of employees attending night school = 12% + 12% = 24%

option b)