#TIME AND WORK-1



 N filling pipes, P1, P2, P3,.....Pn (where n>10)  attached to a tank.The rate of filling of Pi, where  i >1, is equal to thrice the combined rate of filling of all the lower numbered pipes. If the time taken by Pn-3 to fill the tank is 128 minutes, find the time (in minutes) taken by Pn  to fill the tank.

Solution-

It is given that,
Ri = 3*(R1 +R2 +R3 +...+Ri-1)
Where Ri  is the rate of ith pipe.

Now, Tn-3  = 128 min
Rn-3 = 3*(R1 +R2 +R3 +....Rn-4)
Let R1 +R2 +R3 +...+Rn-4 = x
Rn-3 = 3x
Rn-2 = 3*(x+Rn-3) = 12x
Rn-2 = 3*(x + Rn-3 + Rn-2) = 48
Rn = 3*(x + Rn-3  + Rn-2 +Rn-1) = 192x

Now we know that,
rate*time=work
Rn-3 *time = work (constant)
3x*128 = work

Now, for pipe Pn,
Rn *time = work
192x*time = 3x*128
time = (3x*128)/192x
time = 2 minutes ANS

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