3 men are employed to put a fence around the circumference of a circular field. After completing 75% of the total work, due to some urgency of time , they were asked to change the direction of fencing, so that it should be connected to the starting point of fence from the shortest possible path. What will be the total approx time to complete the work if 1 man can fence a length of 4 m in 30 minutes. (Take shortest possible distance as 21√2m)
6 hr
3 hr
5 hr 36 min
None of these
Answer :None of these (Approx 5 hr 22 min)
Solution (Fast Approach)
The shortest distance would be the chord connecting the point, where the work stopped on the circumference, to the starting point.
Draw a circle. Since the fencing was stopped after completion of 3/4 of the work, hence 3/4 part of circle is fenced. Now if you connect the center to the point where work stopped, it would be 90 degree at the center.
According to Pythagoras theorem, if radius = x Then
x2 + x2 = (21√2)2
=>hence: x = 21 m
=>3/4 th of the circle = [(2 x 22 x 21)/22] x (3/4) = 99 m
=>Total fencing = 99 + 21√2 = 128.698 m
1 man can fence 4 m in 30 m
=>Hence 3 men can fence 3x4 = 12 m in 30 min
=>Hence 3 men can fence 128.68 m in (30x128.68)/12 minutes = 321.745 minutes = Approx 5 hr 22 min
|
