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 By: geniuskids (offline)  Sunday, September 01 2013 @ 02:42 AM CDT (Read 1063 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 1.2m-pieces and Log B into 0.9m-pieces, he has no leftover from Log A but there will be 0.6m of Log B left.
If he saws Log A into 1.6m-pieces and Log B into 1.25m-pieces, 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.

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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

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