Quantitative Aptitude - Arithmetic Ability Questions

For any set of 4 points we get a cyclic quadrilateral. Number of ways of choosing 4 points out of 12 points is 12C4 = 495.

Therefore, we can draw 495 quadrilaterals

Let the cost price = Rs 100
then, Marked price = Rs 135

Required gain = 8%,
So Selling price = Rs 108
Discount = 135 - 108 = 27

Discount% = (27/135)*100 = 20%

There are 4 books on fairy tales and they have to be put together. They can be arranged in 4! ways.

Similarly, there are 5 novels.They can be arranged in 5! ways.

And there are 3 plays.They can be arranged in 3! ways.

So, by the counting principle all of them together can be arranged in 4!´5!´3! ways = 17280

Ratio of fruits (by dozen) = 3:2:7

Ratio of fruits (by weight) =  120 :150: 24

Therefore, Ratio of fruits (combined) by weight = 3 x 120 : 2 x 150 : 7 x 24 = 30 : 25 : 14 

4 novels can be selected out of 5 in 5C4 ways.

2 biographies can be selected out of 4 in 4C2 ways.

Number of ways of arranging novels and biographies = 5C4*4C2  = 30

After selecting any 6 books (4 novels and 2 biographies) in one of the 30 ways, they can be arranged on the shelf in 6! = 720 ways.

By the Counting Principle, the total number of arrangements = 30 x 720 = 21600

volume = a3 = 729;

=> a = 9

surface area= 6a2 =  (6 x 9 x 9) = 486 sq.cm

The first letter from the right can be chosen in 26 ways because there are 26 alphabets.

Having chosen this, the second letter can be chosen in 26 ways

The first two letters can chosen in 26 x 26 = 676 ways

Having chosen the first two letters, the third letter can be chosen in 26 ways.

All the three letters can be chosen in 676 x 26 =17576 ways.

It implies that the maximum possible number of five letter palindromes is 17576 because the fourth letter is the same as the second letter and the fifth letter is the same as the first letter.

In this type of questions we need to get the relative speed between them,
The relative speed of the boys = 5.5kmph – 5kmph
= 0.5 kmph

Distance between them is 8.5 km
Time = Distance/Speed
Time= 8.5km / 0.5 kmph = 17 hrs