Quantitative Aptitude - Arithmetic Ability Questions

Here the given number series is 0, 3, 8, 15, 24, ?

The next number in the given series can be found such a way that the number series follows a pattern,

$$\begin{gathered} 22 - 4 = 0 \\ 32 - 6 = 3 \\ 42 - 8 = 8 \\ 52 - 10 = 15 \\ 62 - 12 = 24 \\ 72 - 14 = 35 \\ Hence, the next number in the iven series is 35. \end{gathered}$$

By the rule of alligation:

C.P. of 1 kg sugar of 1st kind      C.P. of 1 kg sugar of 2nd kind 

Therefore, Ratio of quantities of 1st and 2nd kind = 14 : 6 = 7 : 3. 

Let x kg of sugar of 1st kind be mixed with 27 kg of 2nd kind. 

Then, 7 : 3 = x : 27 or x = (7 x 27 / 3) = 63 kg.

Let the no of shots be x. Then, 

Shots fired by A =(5/8)x

Shots fired by B = (3/8)x 

Killing shots by A = 1/3 of (5/8)x  = (5/24)x

Shots missed by B = 1/2 of (3/8)x = (3/16)x 

(3/16)x = 27 ⇒ x =144

Birds killed by A = (5/24)x = (5/24)*144 = 30

 Let S be the sample space

Then, n(S) = 52C2= 1326.

Let E = event of getting 2 kings out of 4.

n(E)  = 52*512*1= 6.

 4C2

=>4*32*1

P(E)=n(E)n(S)=61326=1221

Total time taken    = (160/64 + 160/8)hrs
                           = 9/2 hrs.

Average speed    = (320 x 2/9) km.hr
                         = 71.11 km/hr.