In a hostel, the number of students decreased by 8% and the price of food increased by 20% over the previous year. If each student consumes the same amount of food then By how much should the consumption of food be cut short by every student, so that the total cost of the food remains the same as that of the previous year?
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Took me a second to realize the '8% decrease' and '20% increase' are working in opposite directions. Is the trick to set up (0.92)(1.2)(1-x) = 1? Got 19% but want to make sure I'm not just pattern matching.
Yeah that's the setup I used. The 0.92 and 1.2 multiply to 1.104, so you need to cut that extra 10.4% relative to the new consumption, not just subtract 10.4 from 100.
Classic trap question. I initially just did 20% - 8% = 12% and picked the closest answer. Wrong. The percentages are on different bases so you can't just add/subtract them.
Same mistake here. The word 'every student' is key - you're solving for a per-student cut, not a total.
Learned this the hard way too. Always convert to multipliers before combining percentages.
655-705 seems right for this. Not conceptually hard but the layered percentages make it easy to slip. Respect.
Can someone explain why we don't use 0.92 x 1.2 = 1.104 and then just say 10.4%? I keep getting confused about whether the answer should be ~10% or something else.
Because the 10.4% is the total cost increase at the old consumption level. You need the reduction relative to the NEW cost, so it's 0.104/1.104, which is about 9.4%.
What it tests
Your ability to compute percentage change, percentage of a whole, and to work backwards from a final value.
Common trap
Treating successive percentage changes as additive — a 10% rise then a 10% fall is not back to the start.