Question
If x = 19 and y = 11, then find the value of
(y3 - x3 + 3x2y - 3y2x) .Solution
We know that (a - b) 3 = a3 - b3 - 3a2b + 3b2a
So, in given case, b = x = 19 and y = a = 11
So, required value = (11 - 19) 3 = -512
Pipes ‘A’ and ‘B’ together can fill a tank in 18 hours, while pipe ‘B’ alone can fill it in 36 hours. If pipe ‘C’ takes 12 hours less th...
Tap A can fill a tank in 12 hours. Tap B can fill 20% part of the same tank in 3 hours, whereas Tap C can alone empty a tank in ‘x’ hours. 5/8 part ...
Inlet pipes 'A', 'B' fill a tank in 30 and 15 minutes respectively. Outlet pipe 'C' is 50% less efficient than A. ‘A’ and ‘C’ work for 15 minute...
A cistern has a leak that can empty it in 12 hours. A tap is turned on, which fills water at the rate of 15 liters per hour. Now, the cistern gets empti...
Pipes 'A', 'B', and 'C' working together can fill a tank in 4 hours, while pipes 'B' and 'C' together can fill the same tank in 2...
Pipe X and Y can fill a tank alone in 18 minutes and 24 minutes respectively. If all three pipes X, Y and Z together fill the tank in 8 minutes, find th...
Pipes P and Q alone can fill a tank in 6 hours and 3 hours respectively. When both pipes along with pipe R, an outlet pipe, are opened together, 2/5 of ...
If a tank can be filled by a tap in 12 hours, but due to an outlet, it actually takes 9 hours longer to fill the tank, find the duration in which the ou...
Two pipes A and B can fill a tank in 12 min., and 16 min, respectively. If both the pipes are opened simultaneously, after how much time A should be cl...
Pipe ‘A’ and pipe ‘B’ can fill a cistern in 15 minutes and 36 minutes respectively. Pipe ‘C’ alone can empty the cistern in 12 minutes. If a...