
By: geniuskids (offline) Sunday, September 01 2013 @ 02:42 AM CDT (Read 1047 times)



geniuskids 
Q14: Log A and Log B are of different lengths.
A carpenter wants to saw them into equal number of shorter pieces.
The length of each piece from Log A need not be the same as that of each piece from Log B.
If he saws Log A into 1.2mpieces and Log B into 0.9mpieces, he has no leftover from Log A but there will be 0.6m of Log B left.
If he saws Log A into 1.6mpieces and Log B into 1.25mpieces, he will also have no leftover from Log A but there will be 0.3m of Log B
left . Find the length of Log A.
Answer: 9.6m

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Registered: 11/12/11 Posts: 169





By: echeewh (offline) Sunday, September 01 2013 @ 06:02 AM CDT



echeewh 
Hi <geniuskids>,
Following is my worked solution:
<1st IF cond>
A : B
1.2 : 0.9
12 : 9
4 : 3  (1)
<2nd IF cond>
A : B
1.6 : 1.25
32 : 25  (2)
Given that there was no leftover from Log A in both cases, the 4p of Log A (in the 1st IF) is the same as that (or equal in length) to 32u of Log A (in the 2nd IF).
Thus, 1p = 8u
And, ratio (1) becomes ...
32 : 24  (3)
Comparing ratios (3) , (2), we have ...
24u + 0.6m = 25u + 0.3m
25u  24u = 0.6m  0.3m
1u > 0.3m
Length of Log A = 32u > 32 × 0.3 = 9.6 m
==========
Trust this helps.
Do let me know again if there's further clarification.
Cheers,
Edward

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Registered: 04/21/11 Posts: 627





By: geniuskids (offline) Sunday, September 08 2013 @ 06:56 AM CDT



geniuskids 
Great ! Got it. Thank you so much!

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Registered: 11/12/11 Posts: 169



