Maxima minima

Sum of two numbers is 24.find numbers if product is maximum


Let one number is x and other is 24-x

X(24-x)should be maximum

24x-x^2 Derivative of this function is



Again second derivative =-2

By second derivative test it should be maximum 

At x=12 so other will be also 12 

It satisfied condition  that the product is maximum

Time Management

A alone can do a piece of work in 6 days and B alone in 8 days. A and B undertook to do it for Rs. 3200. With the help of C, they completed the work in 3 days. How much is to be paid to C?
A        Rs. 375 B.        Rs. 400
C.        Rs. 600 D.        Rs. 800


1.A train running at the speed of 60 km/hr crosses a pole in 9 seconds. What is the length of the train?

A.   120 metres B.   180 metres
C.   324 metres D.   150 metres

Answer: Option D


Speed= 60 x 5 m/sec = 50 m/sec.
18 3
Length of the train = (Speed x Time) = 50 x 9 m = 150 m.