A rectangular photo has a 2mm thick frame uniformly around it. If the

E.
Original Area =(X+4)*(Y+4)
since thickness of frame will add on to both sides.

New thickness = (X+2)*(Y+2)

subtracting both :
2X + 2Y +12 =20
X+Y =4

Now since its given length is more so L=3 and B=1

So option E
X+Y

Posted from my mobile device

Let photograph be LxB
Thus
(L+4)(B+4)-(L+2)(B+2)=20
2(L+B)+12= 20
L+B= 4
Since both are integers and L>B thus L=3, B= 1
Hence ratio=3:1

Posted from my mobile device

Let the length of photo be x
Let the breadth of photo be y
Area of photo -xy
Photo has a frame of 2 mm thick around it ,making the length as (x+4) and breadth (y+4)
Area of photo with frame-(x+4)(y+4)
Now the frame size is reduced to 1mm ,making the new area of photo with frame as (x+2)(y+2)
The total area of the photo with frame has been reduced to 20mm2
(x+4)(y+4)-20=(x+2)(y+2)
Solving tbe above equation will refuce to 2x+2y=8
x+y=4
y= 4-x
The ration of length to breadth becomes x/4-x
Checking all the options ,only option E satisty the above equation
There answer is 3/1(E)


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Area of uniform rectangular photo frame with length l, breadth b and width w is given by (l+2w)(b+2w) ............... (I)

Difference in area of photo of width 2mm and photo of width 1mm = 20 mm^2 ............. Given ................ (II)

Using (I) and (II), (l+4)(b+4) - (l+2)(b+2) = 20
that is, lb + 4l + 4b + 16 - lb - 2l - 2b - 4 = 20
that is, 2l + 2b = 8
that is, l + b = 4 ........... (III)

Length and breadth both are integers and length is greater than breadth ............. Given ........ (IV)

Using (III) and (IV), only possible values of length and breadth are 3 and 1 respectively.

We need to find ratio of length and breadth along with original frame,

So, Ratio = (3+2*2)/(1+2*2) = 7/5.

Hence, B is the correct answer.

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