Aptitude - Area - Discussion

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%

Can anyone show how it can be solved by using derivatives? please.

Make it simple yar! Parentage increase increase of rectangle or square will be same.

Assume 10 x 10 original square Area will be 100 simple.

Now increase side length by 20 % will make 12 x 12 square Area will be 144.

So simple should I tell you the correct answer (C) 44.

Assume that total area is 100.

20% of 100 = 120.

20% of 120 = 144.

144 - 100 = 44.

Let original length and breadth be 100.
So new length and breadth are 120
New Area = 120 * 120 so 14400.
Old area = 100 * 100 = 10000.
So diff = 4400.
Error = 4400/(100 * 100) * 100.
So, 44%.

Why all of them taking a length as 100 that and is not a square. Why don't you try it length and breadth with separate values like 100 & 200?

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.

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.

The rational number with recurring decimal expansion 0.12 is __________.

Can anyone answer the question?

If let it 100. It will make more easy.