Porcentaje Inverso

Encontrar el valor original antes de que se aplicara un cambio porcentual.

Aprender

Encontrar el valor original antes de que se aplicara un cambio porcentual.

Reverse percentage problems ask you to work backwards from a final value to find the original. If something increased by X%, the final value equals the original times (1 + X/100). To find the original, divide the final value by this multiplier. This is trickier than forward percentages because you can't simply subtract the percentage.

If Final = Original × (1 + X/100), then Original = Final ÷ (1 + X/100)

After a 20% increase, a price is $120. Original = $120 ÷ 1.20 = $100
After a 25% discount, a price is $60. Original = $60 ÷ 0.75 = $80
After a 10% raise, salary is $55,000. Original = $55,000 ÷ 1.10 = $50,000

Cómo reconocerlo

You're given the final value after a percentage change
You need to find what the value was before the change
Keywords: 'original price', 'was before', 'started at'

Errores comunes

Subtracting the percentage from the final (e.g., $120 - 20% = $96, wrong!)
Using the wrong multiplier (1.20 for increase, 0.80 for 20% decrease)
Confusing increase (multiply by >1) with decrease (multiply by <1)

Resolución paso a paso

Después de un aumento del 25%, un precio es $150. ¿Cuál era el precio original?

Identifica el multiplicador para un aumento del 25%: 1 + 25/100 = 1.25
Plantea la ecuación: Original x 1.25 = $150
Divide el valor final por el multiplicador: $150 / 1.25
Calcula: $150 / 1.25 = $120

Respuesta: $120

Orientación para practicar

Razonamiento Numérico