One 60-second card per skill, in learning order. 10 of 10 cards ready.
Topic 1
Percent of a number · Percent increase and decrease
60-second card
Percent means 'out of 100'. To find x% of a number, multiply by x and divide by 100.
Example: Ravi scored 42 out of 60. 42 ÷ 60 × 100 = 70%.
Remember: Part ÷ whole × 100 gives the percent.
Common mistake: Dividing by the wrong number. The 'of' number (the whole) goes at the bottom.
60-second card
Percent change compares the change with the starting value.
Example: A bag goes from ₹800 to ₹920. Change = 120. 120 ÷ 800 × 100 = 15% increase.
Remember: Always divide by the old (starting) value.
Common mistake: Dividing by the new value, which gives a different, wrong answer.
Topic 2
Profit and loss percent · Discounts
60-second card
Profit or loss percent is always worked out on the cost price (CP).
Example: Bought for ₹40, sold for ₹50. Profit = 10. 10 ÷ 40 × 100 = 25% profit.
Remember: Percent of the cost price, not the selling price.
Common mistake: Dividing the profit by the selling price.
60-second card
A discount is worked out on the marked price (MP), the price on the tag.
Example: Marked ₹1,500, 20% off: 1,500 × 0.8 = ₹1,200.
Remember: Successive discounts multiply; they don't add.
Common mistake: Adding 10% and 20% to get 30%. The real total discount is 28%.
Topic 3
Simplifying ratios · Sharing in a ratio
60-second card
A ratio compares quantities. Simplify it by dividing every part by the same number.
Example: a : b = 2 : 3 and b : c = 4 : 5. Make b = 12: a : b = 8 : 12, b : c = 12 : 15. So a : c = 8 : 15.
Remember: Divide all parts by their highest common factor.
Common mistake: Adding the same number to both parts. That changes the ratio.
60-second card
To share an amount in a ratio, add the parts, then give each person their share of the total.
Example: Share ₹1,200 in 3 : 5. Parts = 8, one part = 150. Shares: ₹450 and ₹750.
Remember: Find one part first; everything else follows.
Common mistake: Dividing the amount by the ratio numbers themselves instead of by their total.
Topic 4
Work per day · Working together
60-second card
If a job takes n days, you do 1/n of it each day. Working with rates makes these sums easy.
Example: 6 workers take 10 days: 60 worker-days. 15 workers need 60 ÷ 15 = 4 days.
Remember: Turn every time into a rate (job per day).
Common mistake: Averaging the days instead of adding the rates.
60-second card
When people work together, add their rates. The time is 1 ÷ (total rate).
Example: Tap fills in 4 h, drain empties in 6 h. Rate = 1/4 − 1/6 = 1/12 per hour, so 12 hours.
Remember: Add rates, never add days.
Common mistake: Adding the days (12 + 6 = 18). Working together must be faster than either alone.
Topic 5
Adding patterns · Other patterns
60-second card
In an adding pattern, the same number is added (or taken away) each time.
Example: 3, 7, 11, 15, ... difference 4. 10th term = 3 + 9 × 4 = 39.
Remember: Write the differences between neighbours first.
Common mistake: Guessing from the first two numbers only. Check the pattern across all of them.
60-second card
If the gaps aren't equal, try multiplying, squares and cubes, or two patterns taking turns.
Example: 3, 5, 9, 17, 33: each is double the last minus 1, so next is 65.
Remember: Check differences, then ratios, then squares, then alternating patterns.
Common mistake: Stopping at the first pattern that fits two numbers without checking the rest.
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