Surds And Indices Q13

13.      If 3(x - y) = 27 and 3(x + y) = 243, then x is equal to:

     A.   0

     B.   2

     C.   4

     D.   6

Answer:

Option : C 

⇒ 3^{x - y} = 27 = 3³⇒ x - y = 3 ....(i)

⇒ 3^{x + y} = 243 = 3⁵⇒ x + y = 5 ....(ii)

On solving (i) and (ii), we get x = 4.