# The average area of 2 rooms I and II are 400 square meters. If one rectangular room(III) area is added then the average area becomes 500 square meters

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The average area of 2 rooms I and II are 400 square meters. If one rectangular room(III) area is added then the average area becomes 500 square meters. If another room IV, whose area is 600 square meters more than the III room, replaces room I, then the average area of II, III and IV room becomes 900 square meters. Find the area of I room.
1. 130  square meters
2. 120 square meters
3. 100 square meters
4. 150 square meters
5. 180 square meters

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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.