Exams

Here by observing the figure, 

we can complete the above incomplete cube with 2 cubes in 2 rows and 2 columns

=> 2 x 4 = 8.

Hence, with 8 small cubes we can complete the cube.

Velocitation is a phenomenon caused by driving for long periods at high speeds. A driver may experience velocitation when coming off of the highway; the change in speed makes him or her think that the car is going much slower than it actually is.

Velocitation is the tendency to be traveling at a speed that is faster than perceived.

Let the ratio amount be 'p'

7p - 3p = 2700

4p = 2700

p = 675

R's Share = 675 × 6 = Rs. 4050

Angle between hands of a clock

When the minute hand is behind the hour hand, the angle between the two hands at M minutes past H 'o clock

=> 30H-M5+M2 degrees

Here H = 4, M = 15 and the minute hand is behind the hour hand.

Hence the angle

 = 30[4-(15/5)]+15/2 = 30(1)+7.5 = 37.5 degrees

Upto first 5 minutes I, J and K will fill => 5[(1/20)+(1/30)+(1/40)] = 65/120

For next 6 minutes, J and K will fill => 6[(1/30)+(1/40)] = 42/120

So tank filled upto first 11 minutes = (65/120) + (42/120) = 107/120
So remaining tank = 13/120

Now at the moment filling with C and leakage @ 1/60 per minute= (1/40) - (1/70) = 3/280.
So time taken to fill remaining 13/120 tank =(13/120) /(3/280) = 91/6 minutes

Hence total time taken to completely fill the tank = 5 + 6 + 91/6 = 26.16 minutes.

RACECAR.

Let the rate be R% p.a.

Then, 5000×r×2100+3000×r×4100=2200

Rate = 10% 

Let the sum be Rs. S.
(S x 18 x 2)/100 - (S x 12 x 2)/100 = 840 => 36S/100 - 24S/100 = 840

=> 12S/100 = 840 => S = 7000.