Aptitude - Area - Discussion

Trick:
If increase in length of breadth & width is x% then the increase in area a' = 2x + (square x)/100.

Quick method: if x=20% then a'.

20 * 2 + (20 * 20 = 4.00) = 44.00.

If x = 4 then a' = 4 * 2 + 0.(4 * 4) = 8 + 0.16 = 8.16%
If x = 5 then a' = 5 * 2 + 0.(5 * 5) = 10 + 0.25 = 10.25.
If x = 6 then a' = 6 * 2 + 0.(6 * 6) = 12 + 0.36 = 12.36.
If x = 7 then a' = 7 * 2 + 0.(7 * 7) = 14 + 0.49 = 14.49.
If x = 8 then a' = 8 * 2 + 0.(8 * 8) = 16 + 0.64 = 16.64.
If x = 9 then a' = 9 * 2 + 0.(9 * 9) = 18 + 0.81 = 18.81.
If x = 10 then a' = 10 * 2 + 0.(10 * 10) = 20 + 1.00 = 21.
If x = 11 then a' = 11 * 2 + 0.(11 * 11) = 22 + 1.21 = 23.21.

Note : When the product is a number of more than three decimals, place a decimal point after two places from the right.

Let,
Original length of rectangle be, x = 100m,
Original breadth of rectangle be, y = 10m,
Original area of the rectangle is, A = 1000 sq. m.

Now, each side is incresed by 20%.

New length of the rectangle is, x1 = 120m,
New breadth of the rectangle is, y1 = 12m,
New area of the rectangle is, A1 = 1440 sq. m.

Therefore, total increase in area = (A1 - A) = (1440 - 1000)m = 440m.

% increase in area;

= (total increase in area / original area) x 100.
= {( A1- A) / A } x 100,
= (440/1000) x 100,
= .44 x 100,
= 44 % (Answer).
Thanks!

The percentage increase in the area of a rectangle, if each of its sides is increased by 20% is:::.

1. Suppose I have 10 of each side and then 20% increased of every side as a question now the 10 comes 12 so now, we have two sides one is new and one is old now we square both old and new sides and we receive 100 for old and 144 for new.

2. Now minus these numbers like.
(144-100) =44.

3. Now we will do percentage of 44 like.
Minus result/previous square nu. *100.
44/100*100=44 answer.
.

What if you don't know what the percentage of increase or decrease is and what if one side is increasing and the other is decreasing?

Let a = percentage change(increase or decrease)on one side and b= percentage change of other side then:
If both sides as are increasing = (a + b) + ab/100.
If both sides are decreasing = (a + b) - ab/100.
If one side is increasing (positive, say a) and one side is decreasing (negative, say b) = a - b - ab/100.

Let's assume that length N width of this rectangle will be 4 and 2 respectively ( you can take any number).

So as per the question, It is increase by 20% by its side.

That means length N width increase to (4+ 4*20%=4.8) & (2+2*20%=2.40) respectively.
Old Sq feet was 4 * 2 = 8
New sq feet is 4.8 * 2.4 = 11.52
Area increased by 11.52-8= 3.52 sq feet.

In percentage,
= area increase/old area * 100.
= 3.52 /8= 44%

As you know that a square is also a rectangle.

We will suppose that its sides are l=100, b=100.

Thus the area will be= l*b = 100*100 = 10000.

Now if there.

Is increment of 20 %.

The new sides are l= 120 and b=120.

Thus the area will be = l*b = 14400.

Difference between the area before increment and after increment.

= 14400-10000 = 4400.

Now the % increase in area is = (4400/10000) *100 = 44%.

Let's assume Length = L cm and Breadth = B cm.

=> Area (old) = L*B = LB....equation (1).

When, Length is increased by 20%, Length = 1.2L.

When, Breadth is increased by 20%, Breadth = 1.2B.

=> Area (increased) = 1.2L*1.2B = 1.44LB.....equation (2).

Using equation (1) and (2).

=> LB (1+% increase/100) = 1.44LB.

=> % increase = (1.44-1)*100 = 0.44*100 = 44 per cent.

There is a much simpler method.

Suppose the length of rectangle = 100 cm & breadth = 50 cm.

So Area equals to 100*50 = 5000.

Now if 20% of both sides are increased then,

New length = 20% of 100 = 120 cm & 20% of 50 = 60 cm.

So, new area = 120*60 = 7200.

Difference = 7200-5000 = 2200.

Percentage increase = (2200\5000)*100 = 44%.

Hi guys i have a easy step to this kind of sum,
if any one side is increased a% mean what is the increment of area can be calculated by the following formula
=2a+(a^2/100)
similarly if a% decrease means area also decreased by
=2a-(a^2/100)

In the above sum side is increased 20 while applying it in the formula
=2*20+(20*20/100)
=40+4
=44

Let,

Length = 10, breadth = 20 unit.

So the area is 200 sq.unit.

Each side increased by 20%.

So length = 10+(10*20/100) = 12 unit.

Breadth = 20+(20*20/100) = 24 unit.

So area = (12*24) = 288 sq.unit.

So percentage area increase = (288-200)/200*100 = 44%.

I think this is the simplest way to do this sum. Hope you will enjoy it.