The area bounded by the lines x 0 y 0 x y 1 2x 3y 6 in square units is ........

Quantitative Aptitude ( CCS) Algebra

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The area bounded by the lines x = 0, y = 0, x + y = 1, 2x + 3y = 6 (in square units) is

2 1/3

2 1/2

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Explanation:

x = 0 is the equation of y-axis.
y = 0 is the equation of x-axis.
Putting x = 0 in x + y = 1, y = 1
Putting y = 0 in x + y = 1, x = 1
Putting x = 0 in 2x + 3y = 6
3y = 6 ⇒ y = 2
Putting y = 0 in 2x + 3y = 6
⇒ 2x = 6 ⇒ x = 3
∴ OB = 1; OA = 1 OD = 3; OC = 2
∴ Required area = ΔOCD – ΔOAB
= 1/2 x 3 x 2 - 1/2 x 1 x 1
= 3 - 1/2 = 2 1/2 sq. units