The average of two numbers is 103. If 2 is added to the greater number, then the ratio of this number to the smaller number becomes 8 : 5.

126

Average age = \(\frac{Total \;sum \;of\; all }{Total \;number\;of \;observations}\)

Sum of 2 numbers = 103 × 2  = 206

2 is added to 2nd number , New sum = 206 + 2 = 208

Ratio of larger to smaller number = 8 : 5

13R = 208

1R = 16

Larger number = 8R

= 8 × 16

= 128

Originally larger number is = 128 - 2 = 126

The correct answer is option (2) : 126