Quantitative Aptitude - Arithmetic Ability Questions

The given number series is 50, 51, 47, 56, 40, ?

$$\begin{gathered} 50 \\ 50 + 12 = 51 \\ 51 - 22 = 47 \\ 47 + 32 = 56 \\ 56 - 42 = 40 \\ 40 + 52 = 65 \end{gathered}$$

Hence, the next number in the given number series is 65.

The smallest value will be obtained by giving x the smallest possible value while y gets the largest possible value. The smallest value for x = 7. This means that y will have to be less than or equal to 3 (so that x + y <11), but we want the largest value of y which is 3.

The difference, x - y will be 4.

Here, n(S) = 52.

Let E = event of getting a queen of club or a king of heart.

Then, n(E) = 2.

P(E) =n(E)/n(S)=2/52=1/26.

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.

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

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