Profit, Loss and Discount

Q1: Multiple Choice Type:

i. Rohit buys an article marked at ₹600 and pays tax = 10%. The total amount paid by him is:

Step 1: Tax = 10% of ₹600 = \(\frac{10}{100} \times 600 = ₹60\)
Step 2: Total amount paid = ₹600 + ₹60 = ₹660
Answer: b. ₹660

ii. The selling price of an article is ₹1,000 and the tax on it is 10%. The increase of its tax if it increases to 15% is:

Step 1: 10% tax = ₹100
Step 2: 15% tax = ₹150
Step 3: Increase = ₹150 − ₹100 = ₹50
Answer: c. ₹50

iii. The selling price of an article is ₹440 inclusive of tax at the rate of 10%, the marked price of the article is:

Step 1: Let marked price = ₹x
\(\frac{110}{100}x = 440 \Rightarrow x = \frac{440 \times 100}{110} = ₹400\)
Answer: b. ₹400

iv. Some goods/services cost ₹800 and rate of GST on it is 12%. If the sales are intra-state, the total amount of bill is:

Step 1: GST = 12% of ₹800 = \(\frac{12}{100} \times 800 = ₹96\)
(CGST = ₹48, SGST = ₹48)
Step 2: Total bill = ₹800 + ₹96 = ₹896
Answer: a. ₹896

v. Some goods/services cost ₹1,500 and rate of GST on it is 8%, the total cost of the bill is:

Step 1: GST = 8% of ₹1,500 = \(\frac{8}{100} \times 1500 = ₹120\)
Step 2: Total bill = ₹1,500 + ₹120 = ₹1,620
Answer: c. ₹1,620

Q2: Ramesh paid ₹345.60 as tax on a purchase of ₹3,840. Find the rate of tax.

Step 1: Tax paid = ₹345.60
Purchase amount (before tax) = ₹3,840
Step 2: Rate of tax is calculated using the formula:
\(\text{Rate of Tax} = \frac{\text{Tax Paid}}{\text{Purchase Amount}} \times 100\)
Step 3: Substituting values:
\(\text{Rate} = \frac{345.60}{3840} \times 100\)
Step 4: \(\text{Rate} = 0.09 \times 100 = 9\%\)
Answer: Rate of tax = 9%

Q3: The price of a washing machine, inclusive of Tax, is ₹13,530/-. If the tax is 10%, find its basic (cost) price.

Step 1: Let the basic cost price be ₹x.
Tax is 10%, so total price including tax = \(x + \frac{10}{100}x = \frac{110x}{100}\)
Step 2: According to the question,
\(\frac{110x}{100} = 13,530\)
Step 3: Multiply both sides by 100:
\(110x = 13,530 \times 100 = 13,53,000\)
Step 4: Divide by 110:
\(x = \frac{13,53,000}{110} = ₹12,300\)
Answer: Basic (cost) price = ₹12,300

Q4: Sarita purchases biscuits costing ₹158 on which the rate of tax is 6%. She also purchases some cosmetic goods costing ₹354 on which the rate of tax is 9%. Find the total amount to be paid by Sarita.

Step 1: Cost of biscuits = ₹158
Tax on biscuits = 6% of ₹158 = \(\frac{6}{100} \times 158 = ₹9.48\)
Total cost of biscuits including tax = ₹158 + ₹9.48 = ₹167.48
Step 2: Cost of cosmetic goods = ₹354
Tax on cosmetics = 9% of ₹354 = \(\frac{9}{100} \times 354 = ₹31.86\)
Total cost of cosmetics including tax = ₹354 + ₹31.86 = ₹385.86
Step 3: Total amount to be paid = ₹167.48 + ₹385.86 = ₹553.34
Answer: Total amount to be paid by Sarita = ₹553.34

Q5: The price of a T.V. set inclusive of tax of 9% is ₹13,407. Find its marked price. If tax is increased to 13%, how much more does the customer has to pay for the T.V. set?

Step 1: Let the marked price be ₹x
Tax is 9%, so the price including tax is:
\(x + \frac{9}{100}x = \frac{109x}{100}\)
Step 2: Given:
\(\frac{109x}{100} = 13,407\)
Step 3: Multiply both sides by 100:
\(109x = 13,407 \times 100 = 13,40,700\)
Step 4: Divide by 109:
\(x = \frac{13,40,700}{109} = ₹12,300\)
Step 5: If tax is increased to 13%, then new total price is:
\(x + \frac{13}{100}x = \frac{113x}{100} = \frac{113 \times 12,300}{100} = ₹13,899\)
Step 6: Extra amount to be paid = ₹13,899 − ₹13,407 = ₹492
Answer: Marked price = ₹12,300
Extra amount to be paid = ₹492

Q6: The price of an article is ₹8,250 which includes tax at 10%. Find how much more or less does a customer pay for the article, if the tax on the article:

Step 1: Let the basic price = ₹x
Given: Total price including 10% tax = ₹8,250
So, \(\frac{110x}{100} = 8250\)
Step 2: Multiply both sides by 100:
\(110x = 8250 \times 100 = 8,25,000\)
Step 3: Divide by 110:
\(x = \frac{825000}{110} = ₹7,500\)
So, base price = ₹7,500

i. Increases to 15%

Step 4: New total price = \(7500 + \frac{15}{100} \times 7500 = 7500 + 1125 = ₹8,625\)
Extra paid = ₹8,625 − ₹8,250 = ₹375
Answer: ₹375 more

ii. Decreases to 6%

Step 5: New total price = \(7500 + \frac{6}{100} \times 7500 = 7500 + 450 = ₹7,950\)
Saved = ₹8,250 − ₹7,950 = ₹300
Answer: ₹300 less

iii. Increase by 2%

New tax rate = 10% + 2% = 12%
New total price = \(7500 + \frac{12}{100} \times 7500 = 7500 + 900 = ₹8,400\)
Extra paid = ₹8,400 − ₹8,250 = ₹150
Answer: ₹150 more

iv. Decreases by 3%

New tax rate = 10% − 3% = 7%
New total price = \(7500 + \frac{7}{100} \times 7500 = 7500 + 525 = ₹8,025\)
Saved = ₹8,250 − ₹8,025 = ₹225
Answer: ₹225 less

Q7: A bicycle is available for ₹1,664 including tax. If the list price of the bicycle is ₹1,600, find:

i. the rate of Tax

Step 1: Tax amount = ₹1,664 − ₹1,600 = ₹64
Step 2: Rate of tax = \(\frac{64}{1600} \times 100 = 4\%\)
Answer: Rate of tax = 4%

ii. the price a customer will pay for the bicycle if the tax is increased by 6%

Step 3: New tax = 4% + 6% = 10%
New price = ₹1,600 + 10% of ₹1,600
= \(1600 + \frac{10}{100} \times 1600 = 1600 + 160 = ₹1,760\)
Answer: New price = ₹1,760

Q8: John belongs to Delhi. He buys goods worth ₹25,000 from a shop in Delhi. If the rate of GST is 5% find how much money in all, will John pay for these goods?

Step 1: Cost of goods = ₹25,000
GST rate = 5%
Step 2: GST amount = \(\frac{5}{100} \times 25000 = ₹1,250\)
Step 3: Total amount payable = ₹25,000 + ₹1,250 = ₹26,250
Answer: John will pay ₹26,250 in all.

Q9: Find the amount of bill for the following inter-state transaction of goods/services: Cost of transaction = ₹30,000, discount = 30% and GST = 28%.

Step 1: Cost before discount = ₹30,000
Step 2: Discount = 30% of ₹30,000 = \(\frac{30}{100} \times 30000 = ₹9,000\)
Step 3: Price after discount = ₹30,000 − ₹9,000 = ₹21,000
Step 4: GST = 28% on ₹21,000 = \(\frac{28}{100} \times 21000 = ₹5,880\)
Step 5: Total amount of bill = ₹21,000 + ₹5,880 = ₹26,880
Answer: Amount of bill = ₹26,880

Q10: For both the following inter-state transaction of services, find the total amount of bill.

i. Cost of services = ₹5,000, discount = 20% and GST = 12%.

Step 1: Cost before discount = ₹5,000
Step 2: Discount = 20% of ₹5,000 = \(\frac{20}{100} \times 5000 = ₹1,000\)
Step 3: Price after discount = ₹5,000 − ₹1,000 = ₹4,000
Step 4: GST = 12% on ₹4,000 = \(\frac{12}{100} \times 4000 = ₹480\)
Step 5: Bill amount = ₹4,000 + ₹480 = ₹4,480

ii. Cost of services = ₹12,500, discount = 40% and GST = 18%.

Step 6: Cost before discount = ₹12,500
Step 7: Discount = 40% of ₹12,500 = \(\frac{40}{100} \times 12500 = ₹5,000\)
Step 8: Price after discount = ₹12,500 − ₹5,000 = ₹7,500
Step 9: GST = 18% on ₹7,500 = \(\frac{18}{100} \times 7500 = ₹1,350\)
Step 10: Bill amount = ₹7,500 + ₹1,350 = ₹8,850
Answer: Total amount of bill ₹4,480 + ₹8,850 = ₹13,330

Q11: A shopkeeper in Indore sells 20 identical articles for ₹450 each. Find the amount of bill if he gives 20% discount and then charges GST = 28%.

Step 1: Price of one article = ₹450
Number of articles = 20
Total cost before discount = ₹450 × 20 = ₹9,000
Step 2: Discount = 20% of ₹9,000 = \(\frac{20}{100} \times 9000 = ₹1,800\)
Price after discount = ₹9,000 − ₹1,800 = ₹7,200
Step 3: GST = 28% on ₹7,200 = \(\frac{28}{100} \times 7200 = ₹2,016\)
Step 4: Total amount of bill = ₹7,200 + ₹2,016 = ₹9,216
Answer: Amount of bill = ₹9,216

Q12: A dealer in Bihar supplied goods to a dealer in Mumbai. The dealer in Mumbai buys. If the rate of GST on the whole is 12%, find how much will the dealer at Mumbai pay to dealer in Bihar.

i. 40 articles for ₹800 each at 30% discount.

Step 1: Cost before discount = 40 × ₹800 = ₹32,000
Step 2: Discount = 30% of ₹32,000 = \(\frac{30}{100} \times 32000 = ₹9,600\)
Step 3: Price after discount = ₹32,000 − ₹9,600 = ₹22,400

ii. 75 articles for ₹1,000 each at 20% discount.

Step 4: Cost before discount = 75 × ₹1,000 = ₹75,000
Step 5: Discount = 20% of ₹75,000 = \(\frac{20}{100} \times 75000 = ₹15,000\)
Step 6: Price after discount = ₹75,000 − ₹15,000 = ₹60,000
Step 7: Total price after discounts = ₹22,400 + ₹60,000 = ₹82,400
Step 8: GST @ 12% on ₹82,400 = \(\frac{12}{100} \times 82400 = ₹9,888\)
Step 9: Total amount payable = ₹82,400 + ₹9,888 = ₹92,288
Answer: The dealer at Mumbai will pay ₹92,288 to the dealer in Bihar.