Quantitative Aptitude - Arithmetic Ability Questions

Three digit number will have unit’s, ten’s and hundred’s place.

Out of 5 given digits any one can take the unit’s place.

This can be done in 5 ways. ...              (i)

After filling the unit’s place, any of the four remaining digits can take the ten’s place.

This can be done in 4 ways. ...              (ii)

After filling in ten’s place, hundred’s place can be filled from any of the three remaining digits.

This can be done in 3 ways. ... (iii) 

So,by counting principle, the number of 3 digit numbers = 5x 4 x 3 = 60

Let the speed of the trains be x and y respectively
length of train1 = 47x
length of train2 = 31y
Relative speed= x + y
Time taken to cross each other = 33 s
=> 47x+31yx+y= 33
=> (47x + 31 y) = 33(x + y)
=> 14x = 2y
=> x/y = 2/14 = 1/7

 = 1:7

Ans.
Given that length of first train + length of second train = 660
Speed of first train : Speed of second train = 5:8 =5x : 8x
Time taken to cross the poll by two trains = 4:3 =4y:3y
Now ,
(5x*4y) + (8x*3y) = 660
44xy = 660
xy = 15
L1 - L2 = 24xy -20xy = 4xy = 60 m

Here I converted the original fraction to a fraction with the denominator being 10, because decimals can be written in the tenths place.

$$\begin{gathered} Divide numerator and denominator with '2' \\ 15 x 22 \\ = 210 \\ = 0.2 \end{gathered}$$

Time required will be in ratio = 5:4

B alone will do it in =16 days

Relative speed = 68-8 = 60 km/hr = 60 X 5 / 18 m/s = 50/3 m/s

Total distance = 150 m

Time taken to pass a man running in same direction = 150 X 3/50 = 9 seconds

let, speed of Ali=X mph and Faizer=Y mph

Now, relative speed when Ali is walking int the same direction with Faizer= (X-Y)mph
hence, according to question, 27/(X-Y)=9 ; solving X-Y=3; --- (1)

Now relative speed when walking in the opposite direction= (X+Y) mph
hence, according to question, 27/(X+y)=3; solving X+Y=9; --- (2)

solving 1 and 2 we get X=6 and Y=3, where X is the speed of Ali.