1. During a sale, a shop offered a discount of 10% on the marked prices of all the items. What would a customer have to pay for a pair of jeans marked at ₹ 1450 and two shirts marked at ₹ 850 each?
Solution:
Total marked price = ₹ (1,450 + 2 × 850)
= ₹ (1,450 +1,700)
= ₹ 3,150
Given that, the discount percentage = 10%
Discount = ₹ \(({10\over 100} \times 3150)\) = ₹ 315
Also, Discount = Marked price − Sale price
₹ 315 = ₹ 3150 − Sale price
∴ Sale price = ₹ (3150 − 315)
= ₹ 2835
Therefore, the customer will have to pay ₹ 2,835.
2. The price of a TV is ₹ 13,000. The sales tax charged on it is at the rate of 12%. Find the amount that Vinod will have to pay if he buys it.
Solution:
On ₹ 100, the tax to be paid = ₹ 12
Here, on ₹ 13000, the tax to be paid will be \(= {12\over 100} \times 13000\)
= ₹ 1560
Required amount = Cost + Sales Tax
= ₹ 13000 + ₹ 1560
= ₹ 14560
Therefore, Vinod will have to pay ₹ 14,560 for the TV.
3. Arun bought a pair of skates at a sale where the discount given was 20%. If the amount he pays is ₹ 1,600, find the marked price.
Solution:
Let the marked price be \(x\).
\(\text{Discount percent} = {\text{Discount}\over \text{Marked Price}} \times 100\)
\(20 ={ \text{Discount}\over x} × 100\)
\(\text{Discount} = {20\over 100} \times x = {x\over5}\)
Discount = Marked price – Sale price
\({x\over 5} = x – 1600\)
\(x – {x\over5} = 1600\)
\({4x\over5} = 1600\)
\(x = 1600 \times {5\over 4}\)
= 2000
Therefore, the marked price was ₹ 2000.
4. I purchased a hair dryer for ₹ 5,400, including 8% VAT. Find the price before VAT was added.
Solution:
The price includes VAT
So, 8% VAT means that if the price without VAT is ₹ 100,
Then, the price including VAT will be ₹ 108
When price including VAT is ₹ 108, original price = ₹ 100
When price including VAT is ₹ 5400, original price = ₹ \(({100\over 108} × 5400)\)
= ₹ 5000
Therefore, the price of the hair dryer before the addition of VAT was ₹ 5,000.
5.An article was purchased for ₹ 1239 including GST of 18%. Find the price of the article before GST was added?
Solution:
Price of an article with GST = ₹1239
GST% = 18%
Let the initial price of the article be ₹ \(x\)
Price of article with GST is ₹ 1239
GST % = 18%
GST = 18% of the initial price of article
So, the initial price of article + GST = 1239
\(x + {18\% \times x} = 1239\)
\(x + ({18x\over100}) = 1239\)
\(({118x\over 100}) = 1239\)
\(x = 1239 × ({100\over 118})\)
\(x =\) ₹\(1050\)
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