Quantitative Aptitude - Arithmetic Ability Questions

$$\begin{gathered} 68 x ? - 3421 = 591 \\ ? = 4012/68 \\ ? = 59 x 59 \\ ? = 3481 \end{gathered}$$

 H   L   C   N    T    A   U   I   O

      L        N          A        I

There are total 131 letters out of which 7 are consonants and 6 are vowels. Also ther are 2L's , 2N's, 2A's and 2I's.

If all the consonants  are together then the numberof arrangements = 7!2!x 1/2! .

But the 7 consonants  can be arranged themselves in  7!2! x 1/2! ways. 

Hence the required number of ways = 7!2!2!2 = 1587600

Let the breadth of the given rectangle be x then length is 2x.
thus area of the given rect is 2x2

after dec 5cm from length and inc 5cm breadth , new lenght becomes 2x-5 and breadth is x+5.thus new area =(2x-5)(x+5)=2x2+5x-25

since new area is 75 units greater than original area thus
2x2+75 = 2x+5x-25
5x=75+25
5x=100
therefore x=20
hence length of the rectangle is 40 cm.

We know that the time difference between India and USA is 9 hrs 30 min.

India is 9:30 hrs ahead of USA.

Time in India = 4:15 + 9:30 = 13:45 PM.

Required Time after 18 hrs = 13:45 + 18 hrs = 7:45 AM.

Hence it is 7:45 AM on the next morning.

Let the numerator be x Then, denominator =  x + 3.

Now. (x + 4)/(x + 3) +4 = 4/5  <=> 5 (x + 4) =  4(x + 7)

=>  x = 8.

The fraction is  8/11.

Let the two parts be (54 - x) and x.

Then, 10 (54 - x) + 22x = 780

=> 12x = 240  

=>  x = 20.

Bigger part = (54 - x)  = 34.