Correct Answer - Option 2 : 30
Suppose the three numbers in A.P. be (a – d), a, (a + d), where, (d > 0)
According to question
⇒ (a – d) a (a + d) = 840
⇒ a (a2 – d2) = 840 ----(1)
Given, the largest number is 7/3 times the smallest, i.e., (a + d) = 7/3 × (a – d)
⇒ 3a + 3d = 7a – 7d
⇒ 4a = 10d
⇒ 2a = 5d
⇒ d = 2a/5 ----(2)
Substituting this value in equation (1), we get –
⇒ a (a2 – 4a2/25) = 840
⇒ 21a3/25 = 840
⇒ a3 = 40 × 25
⇒ a = ∛(8 × 125)
⇒ a = 2 × 5
⇒ a = 10
∴ (a – d + a + a + d) = 3a = (3 × 10) = 30