Quantitative Aptitude - Arithmetic Ability Questions

Originally, let the number of seats for Mathematics, Physics and Biology be 5x, 7x and 8x respectively.
Number of increased seats are (140% of 5x), (150% of 7x) and (175% of 8x).
⇒ [(140/100) × 5x],[(150/100) × 7x] and [(175/100) × 8x]
⇒ 7x, 21x/2 and 14x.

⇒ The required ratio =7x : 21x/2 : 14x
⇒ 14x : 21x : 28x
⇒ 2 : 3 : 4

The given number series 8, 18, 56, 232, 1165 

8

8 x 2 + 2 = 18

18 x 3 + 3 = 57 (not 56)

57 x 4 + 4 = 232

232 x 5 + 5 = 1165

Hence, the odd man in the given series is 56.

Let C.P. be Rs. x.

Then,= >1920-xx*100=x-1280x*100

=>  1920 - x = x - 1280

=>  2x = 3200

=>  x = 1600

 Required S.P. = 125% of Rs. 1600 =Rs(125/100*1600) = Rs2000

Here the given number series is 5  11  21  44  ?  175

Now the given series follows a pattern, that

x2 + 1, x2 - 1, x2 + 2, x2 - 2, x2 + 3, x2 - 3,...

Then the missing number is x2 - 2

= 44 x 2 - 2 = 88 - 2 = 86

Hence, the missing number in the number series is 86.

The word 'OPTICAL' contains 7 different letters.

When the vowels OIA are always together, they can be supposed to form one letter.

Then, we have to arrange the letters PTCL (OIA).

Now, 5 letters can be arranged in 5! = 120 ways.

The vowels (OIA) can be arranged among themselves in 3! = 6 ways.

Required number of ways = (120 x 6) = 720.