Arithmetic Aptitude 4

The required numbers are 27, 36, 45……450.

This is an A.P. with a = 27 and d = 9

Let it has n terms.

Then Tn = 450 = 27 + (n-1) x9

∴ 450 = 27+ 9n - 9

∴ 9n = 432

∴ n = 48

3, 9, 27, 81..............531441 form a G.P. 
with a = 3 and r = 9/3 = 3

Let the number of terms be n

Then 3 x 3n-1 = 531441

∴ 3n = 312

∴ n = 12

Given series is a G. P. with a = 7, r = 7 and n = 6

∴ Sn = a(rn-1) / (r-1)

∴ Sn = 7(76-1) / 6

  Sn = = 137256

Let the numbers be 2X and 9X
Then their H.C.F. is X, so X = 19
∴ Numbers are (2x19 and 9x19) i.e. 38 and 171

Let the no. of Rs. 500 note be X
Then the no. of Rs. 1000 note = 90 – X
∴ 500X + 1000(90 – X) = 71000
∴ 500X + 90000 – 1000X = 71000
∴ 500X = 19000
∴ X = 38

Let the numbers be x, x+2, x+4 and x+6
Then (x + x + 2 + x + 4 + x + 6)/4  = 12
∴ 4x + 12 = 48
∴ x = 9