Quantitative Aptitude - Arithmetic Ability Questions

Let the beds be numbered 1 to 7.

Case 1 : Suppose Anju is allotted bed number 1. 

Then, Parvin cannot be allotted bed number 2. 

So Parvin can be allotted a bed in 5 ways. 

After alloting a bed to Parvin, the remaining 5 students can be allotted beds in 5! ways.

So, in this case the beds can be allotted in 5´5!ways = 600 ways.

Case 2 : Anju is allotted bed number 7. 

Then, Parvin cannot be allotted bed number 6 

As in Case 1, the beds can be allotted in 600 ways.

Case 3 : Anju is allotted one of the beds numbered 2,3,4,5 or 6. 

Parvin cannot be allotted the beds on the right hand side and left hand side of Anju’s bed. For example, if Anju is allotted bed number 2, beds numbered 1 or 3 cannot be allotted to Parvin.

Therefore, Parvin can be allotted a bed in 4 ways in all these cases.

After allotting a bed to Parvin, the other 5 can be allotted a bed in 5! ways.

Therefore, in each of these cases, the beds can be allotted in 4´ 5! = 480 ways. 

The beds can be allotted in (2x 600 + 5 x 480)ways = (1200 + 2400)ways = 3600 ways

The 5 consecutive odd numbers whose average is k are  (k-4), (k-2), k, (k+2), (k+4)

Again the average of (k-4), (k-2), k, (k+2), (k+4), (k+6), (k+8) is (k+2)

Let the diagonals of the squares be 2x and 5x respectively.
Ratio of their areas =  12*2x2:12*5x2=4:25

There are 7 letters in the word DRAUGHT, the two vowels are A and U. Since, the vowels are not to be separated, AU can be considered as one entity. Therefore, the number of letters will be 6 instead of 7. The permutations will be P(6,6) = 6! ways.

But the two vowels A and U can be arranged in two ways, i.e. AU and UA. The required number of arrangements = 2!.6! = 1440 ways.

Given speed = 63 km/hr = 63×518=352 m/s

Let the length of the bridge = x mts

Given time taken to cover the distance of (170 + x)mts is 30 sec.

We know speed = distancetimem/s

⇒352=170+x30

 -->  x = 355 mts.

perimeter of window = πr+2r 

= [(22/7) x (63/2) + 63] = 99+63 = 162 cm

Initially                 CP           profit            SP                MP

                              100           x               (100+x)         133.33

After Change     100           2x             (100+x)   

Now,   Since (100+x)  - 100 = 2x

           76 x= 20%

                         CP            Profit              SP             MP

                        100             20               120           133.33

So,                  300             60               360             400

Again             300            120              420

So the increased selling price = Rs. 420

The number of ways of arranging n beads in a necklace is (n-1)!2=(8-1)!2=7!2 = 2520 

(since n = 8)