Dear Reader, Below are three questions where you have to calculate percentage increase/decrease in areas or sides.

Question 1

The length of a rectangle was increased by 40% and breadth was decreased by 22%. By how much percentage the area would have increased/decreased?

a) Decrease of 0.92% b) increase of 10.92% c) increase of 0.092% d) increase of 9.2%

Answer : d) increase of 9.2%

Solution :

To solve such problems, it is good to assume a particular length and breadth such that their product i.e area comes to 100. In this problem, let us assume the length and breadth to be 20m and 5m respectively. Therefore area = 20 x 5 = 100 sq m.
New length after 40% increase = 20 x 140/100 = 28
New breadth after 22% decrease = 5 x 78/100 = 3.9
New area = 28 x 3.9 = 109.2 sq.m
Difference between the old area and the new area = 109.2 - 100 = 9.2 sq.m.
Percentage increase in area = Increase in area / Original Area x 100% = (9.2 / 100) x 100% = 9.2%

Question 2

Reliance Constructions Company bought a circular land having a radius of 721 m initially. Subsequently they bought extra lands and increased the diameter of the circular ground to 2884 m. Find the percentage increase in the area of circular ground.

a) 100% b) 200% c) 300% d) 400%

Answer : c) 300%

Solution :

Radius of the circular ground initially -- 721 m.
Radius of circular ground subsequently - 2884/2 = 1442.
Area of circular ground initially (22/7 x 721 x 721) =1633786 sq.m.
Area of circular ground subsequently (22/7 x 1442 x 1442) = 6535144 sq.m.
Increase in area of ground = 4901358 sq.m.
Percentage Increase = Increase in area / Original area x 100% = (4901358/1633786) x 100% = 300%

Question 3

Messrs. X's Real Estate bought a rectangular land initially and later on acquired additional land and increased the length by 30%. By how much percentage breadth should be decreased so that the area increases by 17%.

a) 20% b) 10% d) 5% d) none of these.

Answer : b) increase of 17%

Solution :

Similar to first problem, let us assume the length to be 20m and the breadth to be 5m.
Original Area = 20 x 5 = 100 sq.m
New length after 30% increase = 20 x 130/100 = 26m
Let the percentage decrease in breadth be x%. Therefore, new breadth = 5(100 - x) / 100 = (100 - x) / 20 = 5 - x/20
New area = 26(5 - x/20) = 130 - 26x/20
Percentage increase in area = 17 = New area - Old area / Old area x 100% = 130 - 26x/20 - 100 / 100 x 100% = 130 - 26x/20 - 100 = 30 - 26x/20
Simplifying : 17 = 30 - 26x/20
Or 26x/20 = 13
Or x = 13 x 20/26 = 10
Therefore, breadth should be decreased by 10%