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class 8 ganita prakash chapter 1
📖 Textbook Reference: Taxes as Percentages
Tax rates, like the GST (Goods and Services Tax) rate or the Income Tax rates, are also specified as percentages. You may have noticed GST mentioned as part of bills.
This means that the tax is a percentage increase on the cost of the goods, and this extra amount goes to the government.
The Golden Rule: Taxes are ALWAYS calculated on the Sub Total (the total price of all items *before* tax is added). If a bill has both CGST (Central) and SGST (State), both are calculated directly on that base Sub Total.
Check if the calculations are correct in the bill shown.
XY ELECTRICALS SALES RECEIPT
Item: 3 x CFL Bulb @ ₹150.00
Sub Total: ₹450.00
CGST 9%: ₹40.50
SGST 9%: ₹40.50
TOTAL: ₹531.00
XY ELECTRICALS SALES RECEIPT
Item: 3 x CFL Bulb @ ₹150.00
Sub Total: ₹450.00
CGST 9%: ₹40.50
SGST 9%: ₹40.50
TOTAL: ₹531.00
1
A tax is mathematically identical to a "percentage increase." It adds extra cost to the base value.
2
The "Base Value" for taxes is the Sub Total—the total cost of all the goods before any tax is applied.
1
Step 1: Verify the Sub Total. Are 3 bulbs at ₹150 each equal to ₹450? Yes.
2
Step 2: Calculate 9% of 450. (Hint: 1% of 450 is 4.5. Multiply $4.5 \times 9$).
3
Step 3: Add the Sub Total, CGST, and SGST together to see if it equals 531.00.
!
Compounding Taxes (A massive error): Do NOT calculate the SGST on the new amount after CGST is added (e.g., finding 9% of 490.50). In Indian billing, both CGST and SGST are calculated concurrently on the exact same base Sub Total (₹450).
Step-by-Step Verification
1. Check Sub Total: $3 \text{ bulbs} \times ₹150 = ₹450.00$. ✔ Correct
2. Check CGST (9%): $\frac{9}{100} \times 450 = 0.09 \times 450 = ₹40.50$. ✔ Correct
3. Check SGST (9%): $\frac{9}{100} \times 450 = 0.09 \times 450 = ₹40.50$. ✔ Correct
4. Check Final Total: $450.00 + 40.50 + 40.50 = ₹531.00$. ✔ Correct
Ans: Yes, all calculations in the bill are perfectly correct.
You order 2 pizzas at a restaurant for ₹300 each. The restaurant adds a 5% CGST and a 5% SGST.
Calculate the Sub Total, the total Tax Amount, and the Final Bill you have to pay.
Calculate the Sub Total, the total Tax Amount, and the Final Bill you have to pay.
1
Follow the exact same steps as the electrical bill. Find the total cost of the goods first (Sub Total).
2
Apply the percentages to that Sub Total. Since both taxes are 5%, you can calculate them individually or just calculate a flat 10% total tax on the Sub Total!
1
Sub Total = $2 \times 300 = 600$.
2
Total Tax = $5\% + 5\% = 10\%$ of 600.
!
Do not calculate the tax on just one pizza! Tax is applied to the grand subtotal of everything you ordered.
Step-by-Step Calculation
1. Sub Total: $2 \text{ pizzas} \times ₹300 = ₹600$.
2. Tax Amount: CGST (5%) + SGST (5%) = 10% total tax.
$10\% \text{ of } 600 = ₹60$ tax.
3. Final Bill: Sub Total + Tax
$= 600 + 60 = ₹660$.
Ans: Sub Total: ₹600. Tax: ₹60. Final Bill: ₹660.
In the XY ELECTRICALS receipt, why are both the CGST and SGST identical values (₹40.50)?
A. Because 40.50 is the standard minimum tax fee for electrical goods.
B. Because both taxes are charged at the exact same percentage rate (9%) and are applied to the exact same base Sub Total (₹450).
C. Because the SGST is mathematically forced to copy whatever the CGST is.
D. Because 450 divided by 9 is 40.50.
1
If the percentage rate is the same, and the base number is the same, the mathematical result must be the same.
1
Look at the bill: CGST is 9% of 450. SGST is 9% of 450.
!
Option D is mathematically false. $450 \div 9 = 50$, not 40.50. You must multiply by 0.09, not divide by 9.
Logical Explanation
In GST billing, the tax is often split equally between the Central government (CGST) and State government (SGST).
Since both represent a 9% calculation on the original ₹450 subtotal, they will mathematically yield the exact same amount: ₹40.50.
Ans: Option (B)
If a customer bought five CFL bulbs instead of three from XY ELECTRICALS, what would be the mathematical multiplier used to find the new TOTAL PAYABLE amount directly from the new Sub Total?
A. $\text{Sub Total} \times 0.18$
B. $\text{Sub Total} + 18$
C. $\text{Sub Total} \times 1.18$
D. $\text{Sub Total} \times 1.09$
1
A tax is a percentage increase. To find the final amount directly, add the total tax percentage to 100%, and multiply.
Multiplier Logic
The number of bulbs changes the Sub Total, but it does NOT change the tax rate.
Total Tax = $9\% (\text{CGST}) + 9\% (\text{SGST}) = 18\%$.
Therefore, the Final Total is $100\% \text{ (Sub Total)} + 18\% \text{ (Tax)} = 118\%$ of the Sub Total.
Mathematically, this is written as $\text{Sub Total} \times 1.18$.
Ans: Option (C)
