Aptitude - Area - Discussion

7. 

A towel, when bleached, was found to have lost 20% of its length and 10% of its breadth. The percentage of decrease in area is:

[A]. 10%
[B]. 10.08%
[C]. 20%
[D]. 28%

Answer: Option D

Explanation:

Let original length = x and original breadth = y.

Decrease in area
= xy - 80 x x 90 y
100 100
= xy - 18 xy
25
= 7 xy.
25

Decrease % = 7 xy x 1 x 100 % = 28%.
25 xy


Santho said: (Jul 19, 2011)  
x+y-(x*y/100)

Then, 20% + 10%-[20*10/100] = 28%

Nani said: (Aug 16, 2011)  
Please explain clearly anyone of you.

Xyz said: (Sep 8, 2011)  
SANTHO your explanation short and sweet. But why we use x+y in all problems your formula will work or not?

Sabir said: (Dec 12, 2011)  
Nanii ..
Let the original length be 100cm n d breadth be also 100 cm
the lengths n breadths after washing will be 80 and 90 ..
Original area= 100*100 = 10000 cm2
New Area= 80*90 = 7200 cm2
So percentage decrease = (10000-7200)/100 = 2800/100 = 28%
:)

Ajay said: (Jul 26, 2012)  
Let the original length be 20, and breadth = 10.

Therefore original area = 200.

After decrease,

20 reduced to 16 (20% reduction in length).

10 reduced to 9 (10% reduction in breadth).

Therefore 16 x 9 = 144.

200 - 144 = 56.

56/200 = 0.28 i.e. 28%.

Zubair Khan said: (Aug 3, 2012)  
Let width=x and length=y
Area(A1)=xy
New meters after washing-
Width reduced by 20% and length by 10%
Thats why
Width= x-x*(20/100)=x*{1-(2/10)}=x*8/10
Lenght= y-y*(10/100)=y*{1-(1/10)}=y*9/10

New area(A2)= xy*72/100
Area reduced=A1-A2
=xy{1-(72/100)}
=xy*(28/100)
Now it is showing clearly area reduced is 28% ans.

Note= 2% of x means (x*2/100)
=28% of xy means(xy*28/100)

Abc said: (Aug 27, 2012)  
x+y-(x*y/100)------------when area is decreasing


x+y+(x*y/100)---------------when area is increasing,all this type of prblms.

Manoranjan said: (Sep 29, 2012)  
Hi.

Take L=100 nd B=100.

Then 20% in L and 10% in B.

Then new L and B are 80 and 90.

Area=100*100=10000.

New area =7200 then 10000-7200=2800.

Now 2800/10000*100=28 answer.

Rahul said: (Oct 13, 2012)  
If Area, A=XY
the d(A)/A= dX/X + dY/Y
=10+20
=30%

Whats wrong with this method of differentiation?
because answer is not matching.

Sania said: (May 15, 2013)  
But shouldn't the area of a towel be (l+b).

Manish said: (Jul 27, 2013)  
Towel is like rectangle, so area of rectangle is (l*b).

Let l=100, and b =50, so area =l*b =1500.

In question 20% decrease in length and and 10% decrease in breadth.

So new length is 80 and new breadth is 45, so new area =80*45 = 3600.

% decrease in area is (A1-A2) /A1*100 = 28%.

Samuel said: (Aug 9, 2013)  
It can also be solved as thus. Reduction in length = 100 - 20 = 80% which is 80/100.

Reduction in width= 100 - 10 = 90%.

Which is 90/100.

80/100* 90/100* 100 = 72.

100 - 72 = 28%.

Harsha said: (Mar 24, 2014)  
A1 = 100*100 = 10000 (ORIGINAL AREA).

A2 = 80*90 = 7200 (DECREASED IN AREA).

A2-A1 = 2800.

(A2-A1)% = 28%.

Kunal said: (Apr 26, 2014)  
It can also solve by percentage rule.

Suppose a towel area is 100 decreases by 20% and then 10%.
The are of towel= 100 of 20%=20 (say a).

Then, 80 of 10%=8 (say b).
Towels area=a+b.

20+8 = 28% answer.

Sriram said: (Dec 3, 2014)  
So simple by a formula.

x% decrease in length y% decrease in breadth then area change is -x-y+(x*y)/100.

Sam said: (Jul 30, 2016)  
x + y - (x * y/100).

Then, 20% + 10% - [20 * 10/100].
30% - 2% = 28%.

Islam Ansari said: (Sep 4, 2016)  
xy - 18/25xy.
= 7/25xy.

How?

Sreelu said: (Oct 26, 2016)  
There is another simple method.
Let's assume L = 10 and B = 10.
Then area will be 100 (L * B).
When L lost 20% it gets the value 8.
Like that, B lost 10% it gets the value of 9.
So, the new area is 72 i.e (8 * 9).
Then % decrease = 100 - 72 = 28.

Dhanraj said: (Mar 19, 2017)  
How 7/25 came there? Explain it.

Jatin said: (Feb 11, 2018)  
-20-10+20*10/100 = 28%.

Pinku said: (Aug 27, 2019)  
x=a*80/100
y=b*90/100

Area=x*y=80*a*90*b/100*100=72/100(a*b)
decreased area=total area(ab)-72ab/100
=ab-72ab/100
=100-72(ab/100)
=28/100(ab)
= 0 .28ab or 28ab%.

Decreased area by 28%.

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