Question

If a, b, c and d are different positive numbers in H.P., then

• A. a + b > c + d
• B. a + c > b + d
• C. a + d > b + c
• D. None of these

Answer 1

Answer: (C)

a + d > b + c

Answer 2

Since b is the H.M. of a and c, $\frac{a + c}{2}$ > b (A.M. > H.M.).

Again c is the H.M. of b and d, $\frac{b + d}{2}$ > c (A.M. > H.M.).

Adding, we get $\frac{a + c}{2}$+$\frac{b + d}{2}$ > b + c

⇒ a + d > b + c