Arithmetic
⏱ ~3-min readAceMark GuideWhat this topic is really about
The combined rate of A and B is 1/20 of the job per day, and A's individual rate is 1/30. Subtracting A's rate from the combined rate yields B's rate of 1/60 per day, which means B takes 60 days. Distractors like 50 days assume a simple linear difference, which fails to account for the inverse relationship between time and work rate.
The profit of 100 rupees is calculated by subtracting the cost price from the selling price, yielding a 25% profit when divided by the original 400-rupee cost price. A percentage of 20% is incorrect because it mistakenly calculates the profit relative to the selling price instead of the cost price.
See the mechanism
Speed is calculated by dividing the total distance traveled by the time taken, which yields 90 km/h when 360 km is divided by 4 hours. A diagram for this topic isn't available yet — the worked example below walks the same reasoning step by step.
An exam-style question, fully explained
A train travels 360 km in 4 hours. Its speed in km/h:
- Identify what the question tests: A train travels 360 km in 4 hours..
- Speed is calculated by dividing the total distance traveled by the time taken, which yields 90 km/h when 360 km is divided by 4 hours.
- An option like 80 km/h is incorrect because traveling at that rate for 4 hours would only cover 320 km.
Traps the examiner sets
- An option like 80 km/h is incorrect because traveling at that rate for 4 hours would only cover 320 km.
- A percentage of 20% is incorrect because it mistakenly calculates the profit relative to the selling price instead of the cost price.
- Option A is incorrect because 190 is the sum of only the first 19 natural numbers, omitting the final term of 20.
- Distractors like 50 days assume a simple linear difference, which fails to account for the inverse relationship between time and work rate.
- Option A is incorrect because 200 represents the interest for only two years instead of three.
Test your recall
Answer each from memory — you'll see instantly whether you're right and why.
Run a focused 10-question mini-mock on Arithmetic and see it stick.
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