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 _________.
Answer & explanation
Correct answer: option 3
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