Let ' a ' and ' b ' be two numbers where a < b . The geometric mean of these numbers exceeds the smaller number by 12 and the arithmetic mean is smaller than the larger number by 24. Then the value of |b - a| is:

Step-by-step solution

Given a The geometric mean exceeds the smaller number by 12 : ab = a + 12 The arithmetic mean is smaller than the larger number by 24 : a+b 2 = b - 24 a + b = 2b - 48 b - a = 48 Since a To verify, we can find a and b by substituting b = a + 48 into the first equation: a(a+48) = a + 12 Squaring both sides: a^2 + 48a = a^2 + 24a + 144 24a = 144 a = 6 Then b = 6 + 48 = 54 . Thus, |b - a| = |54 - 6| = 48 . Answer: 48