A factory has three belt conveyors fitted in its

Solution

Let conveyor B lifts all the goods in X hours. Conveyor A lifts all goods in X +5 Conveyor C lifts all goods in X – 4 hours. So, conveyor B takes 1/x time to lift in 1 hour Conveyor A takes 1/(x+5) hours to lift in 1 hour Conveyor C takes 1/(x-4) hours to lift in 1 hour. Now, according to the question, to lift all goods, Conveyor A + Conveyor B = Conveyor C 1/(x+5) + 1/x = 1/(x-4) Take LCM on the left side (x+5+x)/x(x+5)= 1/(x-4) 2x+5/x²+5x = 1/(x-4) (2x+5) *(x-4) = x² + 5x 2x²-8x+5x-20 = x² + 5x x²-8x-20 =0 x² - 10x + 2x - 20 = 0 x(x-10) + 2(x-10) = 0 (x-10)*(x+2) = 0 So, x= 10, -2 But x cannot be negative here. So, X = 10 Hence Conveyor B takes X 10 hours. Conveyor A take X + 5 = 10 +5 15 hours Conveyor C takes X-4 hours 10-4 = 6 hours