Two numbers a and b have arithmetic mean 40 and geometric mean is 24. If a > b, then a is

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Solution

The correct option is B 72
A.M. of a and b is 40.
$\frac{a + b}{2} = 40 \Rightarrow a + b = 80$
G.M. of a and b is 24.
$\sqrt{a b} = 24 \Rightarrow a b = 576 (a - b)^{2} = (a + b)^{2} - 4 a b \Rightarrow (a - b)^{2} = 80^{2} - 4 \times 576 \Rightarrow (a - b)^{2} = 6400 - 2304 \Rightarrow (a - b)^{2} = 4096 \Rightarrow (a - b) = 64 a + b = 80 a n d a - b = 64 ∴ a = 72 a n d b = 8 a s a > b$

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