The average of two numbers is 96. If 2 is added to the smaller number, the ratio between the numbers becomes 2 : 3. The smaller number is _________.

75.6

Let smaller number = P & Larger number = Q

Sum of P & Q , ( P+Q) = 2 × 96 = 192    -----(1)

According to question ,

\(\frac{P+2}{Q}\) = \(\frac{2}{3}\) 

3P + 6  = 2Q

3P - 2Q = -6    -----(2)

Multiply equation 1 by 2 and added in equation 2

3P + 2P = 384 - 6 = 378

P = \(\frac{378}{5}\)  = 75.6

So , Smaller number is 75.6