These questions ask for a final value after a starting amount rises or falls by a stated percentage. Some also ask you to recognise calculations that produce the same final value.
Turn the percentage change into a multiplier
Treat the starting value as the whole, or 100%. For an increase of p%, the final value is 100% + p% of the start, so use the multiplier 1 + p/100. For a decrease, 100% - p% remains, so use 1 - p/100. Multiply the starting value by the appropriate multiplier.
| Signal in the question | Calculation for the final value |
|---|---|
| Increase by p% | Start x (1 + p/100) |
| Decrease by p% | Start x (1 - p/100) |
| Find the change first | Start x p/100, then add it for an increase or subtract it for a decrease |
For an increase example, suppose 250 grows by 16%. The multiplier is 1.16, so the final value is 250 x 1.16 = 290. The two-step route agrees: 16% of 250 is 40, then 250 + 40 = 290.
For a decrease example, suppose 160 is reduced by 30%. This leaves 70%, so use 0.70: 160 x 0.70 = 112. Equivalently, the amount removed is 160 x 0.30 = 48, and 160 - 48 = 112. A quick direction check helps: an increased result must be above the start, while a decreased result must be below it.
Avoid these traps
| Tempting route | How to reject it |
|---|---|
| Multiply by p/100 and stop when the final value is required | That product is only the amount added or removed. Keep the original whole by using 1 + p/100 or 1 - p/100, or combine the change with the start. |
| Add or subtract the percentage number as a fixed amount | A percentage is a rate of the starting value, not a fixed number of units. First calculate start x p/100; only that product is the amount to add or subtract. |
| Move in the wrong direction | Words such as increase and raise require a result above the start; decrease, reduce and less require one below it. Check the direction before trusting the arithmetic. |
When several calculations are shown, test each one against the same structure instead of judging by appearance. A one-step multiplier and a two-step change calculation can both be correct if they preserve the starting whole and move in the stated direction.
Try it
A workshop raises its weekly output of 240 units by 15%. Enter the new number of units.
Which calculation does NOT correctly increase 140 by 15%?
- 140 x 1.15
- 140 + 15
- 140 + 0.15 x 140
- 140 + 21
A monthly phone plan costing 85 dollars increases by 8%. Enter the new amount in dollars.