<PRE><B>Question 1166462</B>
&lt;br&gt;
Technically, the statement of the problem is faulty.  There are different solutions possible for different orderings of the four points.&lt;br&gt;
For solving the problem, I will assume the four points are in the given order.&lt;br&gt;
P.....Q.....R.....S&lt;br&gt;
(1) The ratio of PQ:QR is 3:5.  So let PQ=3x and QR=5x:&lt;br&gt;
P&lt;-- 3x --&gt;Q&lt;-- 5x --&gt;R.....S&lt;br&gt;
(2) The ratio of PR:QS is 5:4.  Currently PR is 8x.  Change the scale so that PR is a multiple of 5:&lt;br&gt;
P&lt;-- 15x --&gt;Q&lt;-- 25x --&gt;R.....S&lt;br&gt;
Now PR is 40x; the ratio 5:4 means QS is 32x.  Since QR is 25x, RS is 7x:&lt;br&gt;
P&lt;-- 15x --&gt;Q&lt;-- 25x --&gt;R&lt;-- 7x --&gt;S&lt;br&gt;
Now you can answer the question.  QR is 25x; RS is 7x; PS is 47x.  So&lt;br&gt;
QR:RS:PS = 25:7:47&lt;br&gt;
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