If the sum of 2 numbers is 27 and their product is 182, find the numbe

1.	If the sum of 2 numbers is 27 and their product is 182, find the numbers.1. 20 and 72. 15 and 123. 13 and 144. 19 and 8
Answer» Correct Answer - Option 3 : 13 and 14 Given a + b = 27 ab = 182 Calculation Let the 1st number be a and the 2nd number will be 27 – a Therefore, their product = a (27 – a) It is given that the product of these numbers is 182 Therefore a (27 – a) = 182 ⇒ a² – 27a + 182 = 0 ⇒ a² – 13a – 14a + 182 = 0 ⇒ a(a – 13) – 14(a – 13) = 0 ⇒ (a – 13) (a – 14) = 0 ⇒ a – 13 = 0 or a – 14 = 0 ⇒ a = 13 or a = 14 If first number = 13, then ⇒ Other number = 27 – 13 = 14 If first number = 14, then ⇒ Other number 27 – 14 = 13 ∴ Therefore the numbers are 13 and 14.

If the sum of 2 numbers is 27 and their product is 182, find the numbers.1. 20 and 72. 15 and 123. 13 and 144. 19 and 8

Answer» Correct Answer - Option 3 : 13 and 14

Given

a + b = 27

ab = 182

Calculation

Let the 1st number be a and the 2nd number will be 27 – a

Therefore, their product = a (27 – a)

It is given that the product of these numbers is 182

Therefore a (27 – a) = 182

⇒ a² – 27a + 182 = 0

⇒ a² – 13a – 14a + 182 = 0

⇒ a(a – 13) – 14(a – 13) = 0

⇒ (a – 13) (a – 14) = 0

⇒ a – 13 = 0 or a – 14 = 0

⇒ a = 13 or a = 14

If first number = 13, then

⇒ Other number = 27 – 13 = 14

If first number = 14, then

⇒ Other number 27 – 14 = 13

∴ Therefore the numbers are 13 and 14.

Discussion

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