Quantitative Aptitude - Arithmetic Ability Questions

3 * 5 + 5 * 3 = (2 * 3 - 3 * 5 + 3 * 5) + ( 2 * 5 - 3 * 3 + 5 * 3)

                    = (6 + 10 - 9 + 15) = 22.

[(100 x 35) + (200 x 5)]men can finish the work in 1 day 

Therefore, 4500 men can finish the work in 1 day. 100 men can finish it in  4500/100= 45 days.

This is 5 days behind Schedule

Let the capacity of 1 bucket = x.

Then, capacity of tank = 25x.

New capacity of bucket  = (2/5)x

Required no of buckets = 25x/(2x/5)  = 62.5

Distance covered = 120+120 = 240 m

Time = 12 s

Let the speed of each train = v. Then relative speed = v + v = 2v

2v = distance/time = 240/12 = 20 m/s

Speed of each train = v = 20/2 = 10 m/s

= 10 × 36/10 km/hr = 36 km/hr

Clearly, n(S) = 6 x 6 = 36
Let E be the event that the sum of the numbers on the two faces is divided by 4 or 6.
Then,E = {(1,3),(1,5),(2,2),(2,4),(2,6),(3,1),(3,3),(3,5),(4,2),(4,4),(5,1),(5,3),(6,2),(6,6)}
n(E) = 14.
Hence, P(E) = n(E)/n(S) = 14/36 = 7/18

speed    = (5x5/18)m/sec
             = 25/18 m/sec.

Distance covered in 15 minutes    = (25/18 x 15 x 60)m
                                                 = 1250 m.