Quantitative Aptitude - Arithmetic Ability Questions

If the period between the two months is divisible by 7, then that two months will have the same calender .

 
(a). Oct + Nov  = 31 + 30 = 61 (not divisible by 7)

(b). Apr + May + Jun + Jul + Aug + Sep + Oct = 30 + 31 + 30 + 31 + 31 + 30 + 31  = 214 (not divisible by 7)

(c). Jun + July + Aug + Sep = 30 + 31 + 31 + 30 = 122 (not divisible by 7)

(d). Apr + May + June = 30 + 31 + 30 = 91 (divisible by 7)

Hence, April and July months will have the same calendar.

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.

The given number series is 3, 11, 80, 291, 803

$$\begin{gathered} 3 \\ 3 + 23 = 3 + 8 = 11 \\ 11 + 43 = 11 + 64 = 75 (not 80) \\ 75 + 63 = 75 + 216 = 291 \\ 291 + 83 = 291 + 512 = 803 \end{gathered}$$

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

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