Percentage Problems — Price Reduction, Profit & Loss

Standard Problem: A company reduced the price of an article by 5%. If the original price is ₹P, find the new price.

Formula: New Price = Original Price × (1 − reduction%/100)

Solution: New Price = P × (1 − 5/100) New Price = P × (95/100) New Price = 0.95P

Example: Original price = ₹2000, reduction = 5% New Price = 2000 × 0.95 = ₹1,900 Amount reduced = 2000 − 1900 = ₹100

If the reduced price is known and you need the original:

Formula: Original = Reduced Price / (1 − r/100)

Example: After 5% reduction, price = ₹950. Find original. Original = 950 / 0.95 = ₹1,000

Example: After 20% reduction, price = ₹800. Find original. Original = 800 / 0.80 = ₹1,000

Profit% = (Profit / Cost Price) × 100 Loss% = (Loss / Cost Price) × 100

Example: CP = ₹500, SP = ₹575 Profit = 575 − 500 = ₹75 Profit% = (75/500) × 100 = 15%

Example: CP = ₹800, SP = ₹720 Loss = 800 − 720 = ₹80 Loss% = (80/800) × 100 = 10%

When price is reduced by a%, then by b%: Net change = −a − b + (ab/100)%

Example: 10% reduction, then another 10% reduction: Net = −10 − 10 + (10×10/100) = −20 + 1 = −19% (not −20%)

This is why successive discounts are better for sellers than a single combined discount!