Aptitude and Reasoning Questions

Let the total work be 'W'

As per the given information,

P can complete the work 'W' in 24 days.

=> one day work of P = W/24

And also given that,

The time taken by P to complete one-third of work is equal to time taken by Q to complete half of the work

=> PW/3 = QW/2

=> P's

1 day =    W/24

   ?    =      W/3

=>  ?  = 24W/3W  = 8

=> QW/2 = 8 days

=> Q alone can complete the work W in 16 days

=> P + Q can complete the work in

1/24 + 1/16 = 5/48

=> 48/5 days = 9 3/5 days.

Some teachers can be Doctor and can be Engineer. But there is no common in between Doctor and Engineer. So, option B suits best in which the middle circle denotes teachers.

12 men120 acres36 days54 men?54 days

 As 12 men can reap 120 acres, 54 men will be able to reap more acres in 36 days, 120 acres of land was reaped, so in 54 days, more land will be reaped.

Thus, the numbers of acres that can be reaped by 54 men in 54 days = 5412x120x5436 = 810 acres

Out of 26 alphabets two distinct letters can be chosen in 26P2 ways. Coming to numbers part, there are 10 ways.(any number from 0 to 9 can be chosen) to choose the first digit and similarly another 10ways to choose the second digit. Hence there are totally 10X10 = 100 ways. 

Combined with letters there are 6P2 X 100 ways = 65000 ways to choose vehicle numbers.

The surface area of a cube = 6a2 =  6 side2

New  Surface area = 6 x 1.44a2

Therefore, 0.44a2a2x100 = 44%

When the letters of the word BREAK are arranged in alphabetical order we get the new order of the letters as follows:
A  B  E  K  R
Thus, the letter E satisfies this criteria. This is third in either case whether in the word or in the alphabetical order.