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The product of the three numbers in A.P. is 840 and the largest number is 7/3 times of the smallest number. Then, find the sum of three numbers?
1. 28
2. 30
3. 32
4. 26

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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

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