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?
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