21 set 12

radhika1306 wrote:Working alone at its constant rate, machine K took 3 hours to produce ¼ of the units produced last Friday. Then machine M started working and the two machines, working simultaneously at their respective constant rates, took 6 hours to produce the rest of the unites produced last Friday. How many hours would it have taken machine M, working along at its constant rate, to produce all of the units produced last Friday?
(A) 8
(B) 12
(C) 16
(D) 24
(E) 30

Use numbers .. let there be total of 100 units so in 3 hrs K produced 1/4th of the 100 units.. that is in 3 hrs machine K produced 25 units so in each hr K produces 25/3 units ..

NOw, in 6 hrs M and K together produce the remaining amount of units that is they produce 100-25=75 units ..out of this machine K produced 25/3*6= 50 units .. so in 6hrs M produced 75-50 = 25 units .. that means produces 25/6 units per hour ..

if M were to produce all the 100 units then it would take 100/(25/6) hrs which is equal to 24 hrs .. answer D ..

K worked alone for 3 hours and finished 1/4 of the work. K works another 6 hours (together with M) and so, must have finished another 1/4+1/4 = 1/2 of the work. So, M finished 1 - 1/4 - 1/2 = 1/4 of the work in 6 hours. So, it would take 24 hours for M to finish everything alone.