The obstacle course was very challenging Three out of every

The obstacle course was very challenging. Three out of every 8 contestants fell in the mud at the beginning and gave up. Then 1 out of 5 could not climb over the wall. Then 2 out of 9 could not climb up the rope and dropped out. Finally, 1 out of 10 could not jump over the hurdles and quit. What percent of the contestants made it to the finish line?

Solution

Let N be the number of contestants...

Since we have fractions \"3 out of 8\" , \"1 out of 5\" , \"2 out of 9\" and \"1 out of 10\"

This tells us that the number of contestants is a multiple of the numbers, 8 , 5 , 9 and 10

Lets find LCM of 8,5,9,10 first....

8 = 2^3 * 3^0 * 5^0
5 = 2^0 * 3^0 * 5^1
9 = 2^0 * 3^2 * 5^0
10 = 2^1 * 3^0 * 5^1

LCM = 2^3 * 3^2 * 5^1 = 8*9*5 --> 360

So, the number of contestants is a multiple of 360

Let N = 360p

Three out of every 8 contestants fell in the mud at the beginning and gave up.
So, 5/8th passed --> (5/8)(360p) --> 225p passed

Then 1 out of 5 could not climb over the wall.
So, 4/5th passed --> (4/5)(225p) --> 180p passed

Then 2 out of 9 could not climb up the rope and dropped out.
So, (7/9)th passed --> (7/9)(180p) ---> 140p passed

Finally, 1 out of 10 could not jump over the hurdles and quit.
So, (9/10)th passed --> (9/10)(140p) --> 126p passed

Frraction whi finished = 126p / 360p

126/360

Factor out 6 :

21 / 60

Factor out 3 now :

7/20

So, 7/20th was the fraction that finished