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The sum of two numbers is 120 and their product is 896. Find the numbers .
1. 110 and 10
2. 100 and 20
3. 80 and 40
4. 112 and 8

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Correct Answer - Option 4 : 112 and 8

Given

Sum of two numbers = 120

Product of two numbers = 896

Calculation

Let the numbers be x and y

x + y = 120

⇒ x = 120 - y

xy = 896

⇒ (120 - y)y = 896

⇒ 120y - y2 = 896

⇒ - y+ 120y - 896 = 0

⇒ y2 - 112y - 8y + 896 = 0

⇒ y(y - 112) - 8(y - 112) = 0

(⇒ y - 8)(y - 112) = 0

y = 8 and y = 112

∴ Numbers are 8 and 112

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