Correct Answer - Option 3 : 100 square meters

**Given:**

The average area of I and II room = 400 square meters

The average area of I, II, III room = 500 square meters

Area of IV room = Area of III room + 600 square meters

The average area of II, III and IV room = 900 square meters

**Formula used:**

Average = Sum of all the observation/Total number of observation

**Calculation:**

Area of (I + II) room = 800 ….. (1)

Area of (I + II + III ) = 1500 …..(2)

Area of (II + III + IV) = 2700 ….(3)

From (1) and (2)

⇒ 800 + III = 1500

⇒ III = 1500 – 800

⇒ III = 700

Area of IV room = 700 + 600

= 1300 square metres

From (3)

⇒ II +700 + 1300 = 2700

⇒ II = 2700 – 2000

⇒ II = 700 ….. (4)

From (1) and (4)

⇒ I + 700 = 800

⇒ I = 800 – 700

⇒ I = 100

∴ The area of I room is 100 square meters.