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24 Nov 2018, 10:08
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A rectangular photo has a 2mm thick frame uniformly around it. If the frame size is reduced to 1 mm, the total area of the photograph with the frame is reduced by 20 mm^2. If the length and breadth of the photograph are integers and if the length is greater than breadth, find the ratio of the length and breadth of the photograph including the original frame.
A) 6/5
B) 7/5
C) 5/3
D) 2/1
E) 3/1
24 Nov 2018, 10:16
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Answer E, from given info l+b = 4, and since l>b, l=3, b=1
24 Nov 2018, 10:25
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Let L be length and B be breadth, given that L and B are integers and L > B.
Original frame will have length = L + 2 + 2 = L + 4 and breadth = B + 2 + 2 = B + 4
Smaller frame will have length = L + 1 + 1 = L + 2 and breadth = B + 1 + 1 = B + 2
So, as per condition given in question:
(L + 4)*(B + 4) - (L + 2)*(B + 2) = 20
LB + 4B + 4L + 16 - LB - 2B - 2L - 4 = 20
2*(L + B) + 12 = 20
L + B = 4
Now, possible combinations of integers for L and B can be 1 + 3 = 4, 2 + 2 = 4 or 3 + 1 = 4.
But it is given that L > B, so only case possible is 3 + 1 = 4. Hence L = 3 and B = 1
Ratio asked = (L + 4) / (B + 4) = (3+4)/(1+4) = 7/5
IMO Option B! Is there a shortcut though?
Original frame will have length = L + 2 + 2 = L + 4 and breadth = B + 2 + 2 = B + 4
Smaller frame will have length = L + 1 + 1 = L + 2 and breadth = B + 1 + 1 = B + 2
So, as per condition given in question:
(L + 4)*(B + 4) - (L + 2)*(B + 2) = 20
LB + 4B + 4L + 16 - LB - 2B - 2L - 4 = 20
2*(L + B) + 12 = 20
L + B = 4
Now, possible combinations of integers for L and B can be 1 + 3 = 4, 2 + 2 = 4 or 3 + 1 = 4.
But it is given that L > B, so only case possible is 3 + 1 = 4. Hence L = 3 and B = 1
Ratio asked = (L + 4) / (B + 4) = (3+4)/(1+4) = 7/5
IMO Option B! Is there a shortcut though?
