The product of three consecutive positive numbers is divided by each o

1.	The product of three consecutive positive numbers is divided by each of them in turn, the sum of the three quotients will be 74. What will be sum of three numbers?1. 122. 153. 174. 19
Answer» Correct Answer - Option 2 : 15 Let the three consecutive numbers be x, x + 1 and x + 2 Now, the product of these three numbers = x (x + 1) (x + 2) The product is divided by each of them and sum of three quotients is 74 ∴ (x + 1) (x + 2) + x (x + 1) + x (x + 2) = 74 ⇒ x² + 2 + 3x + x² + x + x² + 2x = 74 ⇒ 3x² + 6x = 74 – 2 ⇒ x² + 2x – 24 = 0 ⇒ x² + 6x – 4x – 24 = 0 ⇒ x(x + 6) – 4(x + 6) = 0 ⇒ x = -6, 4 Rejecting -6 as number is positive ∴ Three consecutive numbers are 4, 5 and 6 Sum = 4 + 5 + 6 = 15 ∴ The sum of three numbers is 15

The product of three consecutive positive numbers is divided by each of them in turn, the sum of the three quotients will be 74. What will be sum of three numbers?1. 122. 153. 174. 19

Answer» Correct Answer - Option 2 : 15

Let the three consecutive numbers be x, x + 1 and x + 2

Now, the product of these three numbers = x (x + 1) (x + 2)

The product is divided by each of them and sum of three quotients is 74

∴ (x + 1) (x + 2) + x (x + 1) + x (x + 2) = 74

⇒ x² + 2 + 3x + x² + x + x² + 2x = 74

⇒ 3x² + 6x = 74 – 2

⇒ x² + 2x – 24 = 0

⇒ x² + 6x – 4x – 24 = 0

⇒ x(x + 6) – 4(x + 6) = 0

⇒ x = -6, 4

Rejecting -6 as number is positive

∴ Three consecutive numbers are 4, 5 and 6

Sum = 4 + 5 + 6 = 15

∴ The sum of three numbers is 15

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