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Anglo Chinese SA 2 paper 2 Question 18

There were a total of 655 black and red pens in a box. The number of black pens to the number of red pens was 3:4. Some green pens and purple pens were put into the box. For every 5 red pens that were already in the box, 12 purple ones were added. Then the final number of black pens and green pens was 1/4 the final number of red pens and purple pens. Find the ratio of the number of green pens to the number of purple pens. Give your answer in its simplest form.

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