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In a factory, there are 45 permanent staff and 30 temporary staff. By what percentage should the number of temporary staff be increased so that it becomes equal to the number of permanent staff?
30%
40%
50%
60%
50%
Use the ratio of increase: The difference is 45тИТ30=15. The increase relative to temporary staff is 3015тАЛ=21тАЛ=50%.
Permanent staff = 45, Temporary staff = 30
Percentage┬аIncrease=(Initial┬аValueTarget┬аValueтИТInitial┬аValueтАЛ)├Ч100%
Use the ratio of increase: The difference is 45тИТ30=15. The increase relative to temporary staff is 3015тАЛ=21тАЛ=50%.
Students often calculate the increase relative to the permanent staff (45) instead of the temporary staff (30), leading to the incorrect answer of 33.33%.
Identify the required increase
To make the number of temporary staff equal to the permanent staff, the new count must be 45. The required increase is 45тИТ30=15.
15
Calculate the percentage increase
Divide the increase by the original number of temporary staff and multiply by 100 to convert to a percentage.
3015тАЛ├Ч100%=0.5├Ч100%=50%
C is correct because the required increase of 15 staff members over the base of 30 results in a 50% growth.
This concept of 'base value' is critical in profit/loss (cost price as base) and relative speed problems in Time, Speed, and Distance.