Five bells begin to toll together and toll respectively at intervals of 6, 7, 8, 9 and 12 seconds. How many times they will toll together in one hour , excluding the one at the start?

I. 2x ² ?21x + 54 = 0(x -6)(2x -9)x =+6, +9/2

II. y ² ?14y + 49 = 0(y-7) (y-7)y = +7, +7y > x

Let the normal speed be x km/h, then 

80 x - 80 ( x + 4 ) = 1

? x 2 + 4 x - 320 = 0

?x (x + 20) - 16 (x + 20) = 0

(x + 20 ) (x - 16) =0

x = 16 km/h

 Therefore (x + 4) = 20 km/h

 Therefore increased speed = 20 km/h

Take nearest values
?580×?510+ 49.999 x 3.999=?
24x 8 + 200 = 392

Let the length of the train be L metres and speeds of the train Arun and Sriram be R, A and S respectively, then 

        L R - A = 36 ---------- (i) 

and  L R + K = 24 ---------(ii)

From eq.(i) and (ii)

              3(R - A ) = 2 (R + K) 

?  R = 3A + 2K 

In 30 minutes (i.e 1800 seconds), the train covers 1800R (distance) but the Arun also covers 1800 A (distance) in the same time. Therefore distance between Arun and Sriram, when the train has just crossed Sriram

               = 1800 ( R - A) - 24 ( A + K)

 Time required =  1800 ( R - A ) - 24 ( A + K ) ( A + K )

= (3600 - 24) = 3576 s                            

The hour hand moves from pointing to 12 to pointing to half way between 2 and 3. The angle covered between each hour marking on the clock is 360/12 = 30. Since the hand has covered 2.5 of these divisions the angle moved through is 75.

500+2000÷40×50=?

?= 500+(2000÷40)×50

?= 500+50×50

?=500+2500

?=3000

Let the speeds of two trains be 7X and 8X km/hr.

8x = 400/4

=> x= 12.5 km/hrX=4004=>X=12.5Km/hr

So speed of first train is 12.5*7 = 87.5 km/hr

Amy can travel clockwise or anticlockwise on the diagram.

Clockwise, she has no choice of route from A to B, a choice of one out of two routes from B to C, and a choice of one out of two routes from C back to A. This gives four possible routes.

Similarly, anticlockwise she has four different routes.

Total routes = 8