The Logic Behind the Math: The Unitary Method vs. Multiplier

The standard way to calculate tax is $Base \times (Rate/100)$. However, for speed, we use the Total Multiplier (M).If GST is $18\%$, $M = 1.18$.$\text{Total Price} = \text{Base Price} \times 1.18$.

Step-by-Step Solved Example (The "Reverse" Problem)

Problem: A student buys a graphing calculator for ₹11,800, which includes $18\%$ GST. Find the original price and the tax amount.

• Step 1: Identify the Total ($T$). $T = 11,800$.
• Step 2: Identify the Rate ($R$). $R = 18\%$.
• Step 3: Define the Multiplier ($M$). $M = 1 + (18/100) = 1.18$.
• Step 4: Back-calculate the Base ($B$). $B = T / M$.$B = 11,800 / 1.18$.
• Step 5: Solve. Shift decimals: $1,180,000 / 118 = 10,000$.
• Step 6: Find Tax Amount. $11,800 - 10,000 = ₹1,800$.

Alternative Methods: The Fractional Approach

Common tax rates can be converted to fractions for faster cancellation:

• $5\%$ GST $\to$ Multiply by $21/20$
• $12\%$ GST $\to$ Multiply by $28/25$
• $20\%$ (Luxury) $\to$ Multiply by $6/5$

Using fractions is often superior when the Base Price is a multiple of $5$ or $2$, which is common in exam paper design.

Exam Trap Alert: The "Tax on Tax" Fallacy

A classic trap involves two successive percentage increases.

Trap: If a price increases by $10\%$ and then a $10\%$ tax is added, the total increase is NOT $20\%$.It is $1.10 \times 1.10 = 1.21$, or a $21\%$ increase.In JEE Physics, this is the same logic as Successive Magnification in a compound microscope.

Practice Problem (JEE Logic)

Question: A wholesaler gives a $20\%$ discount on the list price of an item. The retailer then adds a $12\%$ GST on the discounted price. If the final price paid by the consumer is ₹8,960, find the original list price.