In a hostel, every resident prefers exactly one of tea and coffee, and the ratio of tea drinkers to coffee drinkers is . Then 12 new residents, all coffee drinkers, move in and 5 tea drinkers move out. The ratio of tea drinkers to coffee drinkers is now .
How many tea drinkers were there in the hostel originally?
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Solution MCQ · 1 mark · −⅓ if wrong
Answer: (C) 80
Method. Give the original ratio a unit: tea , coffee . After the change, tea and coffee , and these are in the ratio :
So there were tea drinkers and coffee drinkers. Check: after the change, .
The trap. Because the tea side of the ratio is 5 both before and after, it is tempting to say "coffee went from 3 parts to 4 parts, so one part is 12" and answer . That shortcut is valid only when the tea count is unchanged. Here both groups changed, so a "part" before and a "part" after are different sizes; you must write one equation in .
What was tested. Turning a ratio into counts with a single unknown and re-imposing the second ratio on the changed counts, and then answering the exact quantity asked (original tea, not new tea or the total).
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