Question

Length of a rectangle increases by 20 % and width decreases by 10%.By what % does the area change?

Answer 1

Let length be 10

And breadth be 10

Area 100

Now length is increased by 20%

New length 12

And breadth is decreased by 10%

New breadth is 9

New area is 12*9=108

Change in area 108-100= 8

So overall area increases by 8%

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2nd method

Use this formula (x+y+xy/100)

Where x,y are percentage change

Use positive for increment

Use negative for decrement.

And observe overall result

In above question

x=20, y= -10

So overall change

(20 -10 +(20)*(-10)/100)

(10- 200/100)

(10- 2)

8

Result is +ve so overall area increases by 8%