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The first two pieces are in the ratio 3:5. Their weight can be taken as 3x gms and 5x gms respectively.
Of these two 5x gms piece is further divided in the ratio 5:7
So these pieces will be (5/12)5x and (7/12)5x
= (25/12)x gms and (35/12)x GMs.
The ratio of all the three pieces is
3x : (25/12)x : (35/12)x
Multiply by 12 throughout
36x: 25x: 35x= 36:25:35
So, the ratio of all the three pieces is 36:25:35
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