Previous Year Questions

Let the length and breadth of the door are 'nx' cm and n(x - 3) cm respectively and the length of room A and B are 'a' cm and 'a + 40' cm respectively.

Breadth of the rooms = 150% of nx = '1.5nx' cm

Height of the rooms = (1.5nx - 60) cm

Area of area of four walls room B including door - Area of four walls of room A including door = 1.92 m²

2*(1.5nx - 60) * [a + 40 + 1.5nx] - 2*(1.5nx - 60) * [a + 1.5nx] = 19200 cm²

(1.5nx - 60) [a + 40 + 1.5nx - a - 1.5nx] = 9600

1.5nx - 60 = 9600/40

1.5nx = 240 + 60

nx = 200

Sum of the length of breadth of the door < 300 cm

nx + n(x - 3) < 300

2nx - 3n < 300

2*200 - 3n < 300

3n > 100

n > 33.33

So, the value of n and x can be (40, 5) and (50, 4). [Since x > 3, so the value can't be (100, 2)]

When (n, x) = (40, 5)

Area of the door = (40*5)*(40*2) = 16000 cm²

When (n, x) = (50, 4)

Area of the door = (50*4)*(50*1) = 10000 cm²

So, the range of the area of the door = (10000, 16000)