Quantitative Aptitude - Arithmetic Ability Questions

 H   L   C   N    T    A   U   I   O

      L        N          A        I

There are total 131 letters out of which 7 are consonants and 6 are vowels. Also ther are 2L's , 2N's, 2A's and 2I's.

If all the consonants  are together then the numberof arrangements = 7!2!x 1/2! .

But the 7 consonants  can be arranged themselves in  7!2! x 1/2! ways. 

Hence the required number of ways = 7!2!2!2 = 1587600

Let the total population be 'P'

P x (96/100) = 23040

P = 240 * 100

P = 24000.

In 12 hours, they are at right angles 22 times.
In 24 hours, they are at right angles 44 times.

Let original length = x and original breadth = y.  

Decrease in area = xy - 80100x×90100y = (7/25)xy

Decrease % =    (7/25)xy * (1/xy) * 100 = 28%

Let x128=162x

Then, $$\begin{gathered} x2=128×162 =64×2×18×9 \\ =82×62×32 = 8×6×3 =144 \end{gathered}$$

∴x=12

Let 'd' be the distance and 's' be the speed and 't' be the time
d=sxt
45 mins = 3/4 hr and 48 mins = 4/5 hr
As distance is same in both cases;
s(3/4) = (s-5)(4/5)
3s/4 = (4s-20)/5
15s = 16s-80
s = 80 km.
=> d = 80 x 3/4 = 60 kms.

One person can select one house out of 3= 3C1 ways =3.

Hence, three persons can select one house out of 3 in 3 x 3 x 3 =9.

Therefore, probability that all thre apply for the same house is 1/9