Previous Year Questions

Let the number of bricks manufactured by company C = a

Number of baked bricks sold by company D = a - 4500

Number of baked bricks sold by company C = 80/(80+100) * (100 - 40)/100 * a = 4a/15

Now,

Number of baked bricks sold by company C - Number of baked bricks sold by company D = 100

4a/15 - (a - 4500) = 100

11a/15 = 4400

a = 6000

Number of baked bricks sold by company D = 6000 - 4500 = 1500

Number of baked bricks manufactured by company D = 1500 * (100+50)/50 = 4500

(X² + Y²) = 4500

I: X + 10 = 2Y + 8

X = 2Y - 2

(2Y - 2)² + Y² = 4500

5Y² - 8Y + 4 = 4500

5Y² - 8Y - 4496 = 0

Y = 4(1 ± √1406)/5 (not possible)

II: 3X - Y = 75% of 200

Y = 3X - 150

X² + (3X - 150)² = 4500

X² - 90X + 1800 = 0

(X - 30)(X - 60) = 0

X = 30, 60

Y = 3*30 - 150 = -60 (not possible)

Y = 3*60 - 150 = 30

The values of X are Y are positive integers.

III: 20% of (X + Y) = 540/(X - Y)

(X + Y)(X - Y) = 2700

X² - Y² = 2700

X² + Y² = 4500

From both equations -

X² = 3600 => X = 60

Y² = 900 => Y = 30

The values of X are Y are positive integers.

Hence option 'e' is correct.