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# Divide 20 into Two Parts Such that Three Times the Square of One Part Exceeds the Other Part by 10. - ICSE Class 10 - Mathematics

#### Question

Divide 20 into two parts such that three times the square of one part exceeds the other part by 10.

#### Solution

Let the two parts be x and y.
From the given information,
x + y = 20 ⇒ y = 20 – x
3x2 = (20 – x) + 10
3x2 = 30 – x
3x2 + x – 30 = 0
3x2 – 9x + 10x – 30 = 0
3x(x – 3) + 10(x – 3) = 0
(x – 3) (3x + 10) = 0
x = 3, -10/3
Since, x cannot be equal to -10/3, so, x = 3.
Thus, one part is 3 and other part is 20 – 3 = 17.

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#### APPEARS IN

Selina Solution for Selina ICSE Concise Mathematics for Class 10 (2018-2019) (2017 to Current)
Chapter 6: Solving (simple) Problems (Based on Quadratic Equations)
Ex.6A | Q: 12

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Solution Divide 20 into Two Parts Such that Three Times the Square of One Part Exceeds the Other Part by 10. Concept: Quadratic Equations.
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