Profit & Loss, Discount & Tax

Q1: The marked price of a refrigerator is ₹16450. The shopkeeper offers an off-season discount of 16% on it. Find its selling price.

Step 1: Given,
Marked Price (M.P.) = ₹16450
Discount = 16%
Step 2: Calculate the discount amount: \[ \text{Discount} = \frac{16}{100} × 16450 = ₹2632 \]Step 3: Selling Price (S.P.) = Marked Price − Discount \[ S.P. = 16450 − 2632 = ₹13818 \]Answer: The selling price of the refrigerator is ₹13818.

Q2: The price of a sweater was slashed down by a shopkeeper from ₹850 to ₹731. Find the rate of discount given by him.

Step 1: Given,
Original Price (Marked Price, M.P.) = ₹850
Selling Price (S.P.) = ₹731
Step 2: Calculate the discount amount: \[ \text{Discount} = \text{M.P.} − \text{S.P.} = 850 − 731 = ₹119 \]Step 3: Calculate the rate of discount: \[ \text{Rate of Discount} = \frac{\text{Discount}}{\text{M.P.}} × 100 = \frac{119}{850} × 100 ≈ 14\% \]Answer: The rate of discount given by the shopkeeper is 14%.

Q3: Find the rate of discount being given on a mini toy-gun whose selling price is ₹345 after deducting a discount of ₹30 on its marked price.

Step 1: Given,
Selling Price (S.P.) = ₹345
Discount = ₹30
Step 2: Find the Marked Price (M.P.): \[ \text{M.P.} = \text{S.P.} + \text{Discount} = 345 + 30 = ₹375 \]Step 3: Calculate the rate of discount: \[ \text{Rate of Discount} = \frac{\text{Discount}}{\text{M.P.}} × 100 = \frac{30}{375} × 100 = 8\% \]Answer: The rate of discount given on the mini toy-gun is 8%.

Q4: After allowing a discount of 15%, a baby-suit was sold for ₹1156. Find its marked price.

Step 1: Given,
Selling Price (S.P.) = ₹1156
Discount = 15%
Step 2: Let Marked Price (M.P.) = ₹x
Step 3: Relation between S.P. and M.P.: \[ S.P. = M.P. – \text{Discount} = M.P. × \left(1 – \frac{15}{100}\right) = x × \frac{85}{100} = \frac{85x}{100} \]Step 4: Substitute the value of S.P.: \[ 1156 = \frac{85x}{100} \]Step 5: Solve for \(x\): \[ x = \frac{1156 × 100}{85} = \frac{115600}{85} = ₹1360 \]Answer: The marked price of the baby-suit is ₹1360.

Q5: A calculator was bought for ₹ 435 after getting a discount of 13%. Find the marked price of the calculator.

Step 1: Given,
Cost Price (after discount) = ₹435
Discount = 13%
Step 2: Let Marked Price (M.P.) = ₹x
Step 3: Since discount is 13%, the cost price is 87% of marked price: \[ 435 = \frac{87}{100} × x = \frac{87x}{100} \]Step 4: Solve for \(x\): \[ x = \frac{435 × 100}{87} = \frac{43500}{87} = ₹500 \]Answer: The marked price of the calculator is ₹500.

Q6: A dealer marked his goods 35% above cost price and allowed a discount of 20% on the marked price. Find his gain or loss per cent.

Step 1: Let Cost Price (C.P.) = ₹100 (assumed for calculation)
Step 2: Marked Price (M.P.) = C.P. + 35% of C.P. = \(100 + 35 = ₹135\)
Step 3: Discount allowed = 20% on M.P.
Selling Price (S.P.) = M.P. − 20% of M.P. = \(135 – \frac{20}{100} × 135 = 135 – 27 = ₹108\)
Step 4: Gain or Loss = S.P. − C.P. = ₹108 − ₹100 = ₹8 (Gain)
Step 5: Gain percent = \(\frac{\text{Gain}}{\text{C.P.}} × 100 = \frac{8}{100} × 100 = 8\%\)
Answer: The dealer gains 8% on his goods.

Q7: An article was marked above cost price and a discount of 35% was given on its marked price. Find the gain or loss per cent made by the shopkeeper.

Step 1: Let the cost price (C.P.) = ₹100 (assumed for simplicity).
Step 2: Marked Price (M.P.) = C.P. + 40% of C.P. \[ M.P. = 100 + 40 = ₹140 \]Step 3: Discount = 35% on marked price.
Selling Price (S.P.) = M.P. − 35% of M.P. \[ S.P. = 140 – \frac{35}{100} × 140 = 140 – 49 = ₹91 \]Step 4: Calculate gain or loss: \[ \text{Gain/Loss} = S.P. – C.P. = 91 – 100 = -9 \] Since it is negative, it is a loss of ₹9.
Step 5: Calculate loss percent: \[ \text{Loss \%} = \frac{9}{100} × 100 = 9\% \]Answer: The shopkeeper incurs a loss of 9%.

Q8: A dealer purchased a washing machine for ₹7660. After allowing a discount of 12% on its marked price, he gains 10%. Find the marked price.

Step 1: Given,
Cost Price (C.P.) = ₹7660
Discount = 12% on Marked Price (M.P.)
Gain = 10% on Cost Price
Step 2: Let the Marked Price be ₹x.
Step 3: Selling Price (S.P.) after discount: \[ S.P. = M.P. – \text{Discount} = x – \frac{12}{100} × x = \frac{88}{100}x = \frac{22}{25}x \]Step 4: Selling Price with 10% gain on cost price: \[ S.P. = C.P. + 10\% \text{ of } C.P. = 7660 + \frac{10}{100} × 7660 = 7660 + 766 = ₹8426 \]Step 5: Equate the two expressions for S.P.: \[ \frac{22}{25} x = 8426 \]Step 6: Solve for \(x\): \[ x = \frac{8426 × 25}{22} = \frac{210650}{22} = ₹9575 \]Answer: The marked price of the washing machine is ₹9575.

Q9: A shopkeeper bought a sewing machine for ₹3750. After allowing a discount of 10% on its marked price, he gains 26%. Find the marked price of the sewing machine.

Step 1: Given,
Cost Price (C.P.) = ₹3750
Discount = 10% on Marked Price (M.P.)
Gain = 26% on Cost Price
Step 2: Let the Marked Price be ₹x.
Step 3: Selling Price (S.P.) after discount: \[ S.P. = M.P. – 10\% \text{ of } M.P. = x – \frac{10}{100} × x = \frac{90}{100}x = \frac{9}{10}x \]Step 4: Selling Price with 26% gain on cost price: \[ S.P. = C.P. + 26\% \text{ of } C.P. = 3750 + \frac{26}{100} × 3750 = 3750 + 975 = ₹4725 \]Step 5: Equate the two expressions for S.P.: \[ \frac{9}{10} x = 4725 \]Step 6: Solve for \(x\): \[ x = \frac{4725 × 10}{9} = \frac{47250}{9} = ₹5250 \]Answer: The marked price of the sewing machine is ₹5250.

Q10: After allowing a discount of 10% on the marked price, a trader still makes a profit of 17%. By what per cent is the marked price above cost price?

Step 1: Let Cost Price (C.P.) = ₹100 (assumed for simplicity).
Step 2: Let Marked Price (M.P.) = ₹x.
Step 3: Selling Price (S.P.) after 10% discount on M.P.: \[ S.P. = x – \frac{10}{100} × x = \frac{90}{100}x = \frac{9}{10}x \]Step 4: Since trader makes 17% profit on cost price: \[ S.P. = C.P. + 17\% \text{ of } C.P. = 100 + 17 = ₹117 \]Step 5: Equate the two expressions for S.P.: \[ \frac{9}{10} x = 117 \]Step 6: Solve for \(x\): \[ x = \frac{117 × 10}{9} = \frac{1170}{9} = 130 \]Step 7: Calculate how much M.P. is above C.P.: \[ \text{Marked Price is above Cost Price by } = x – 100 = 130 – 100 = 30 \]Answer: The marked price is 30% above the cost price.

Q11: After allowing a discount of 12% on the marked price, a shopkeeper still gains 21%. By what per cent is the marked price above cost price?

Step 1: Let Cost Price (C.P.) = ₹100 (assumed).
Step 2: Let Marked Price (M.P.) = ₹x.
Step 3: Selling Price (S.P.) after discount: \[ S.P. = x – \frac{12}{100} × x = \frac{88}{100}x = \frac{22}{25}x \]Step 4: Selling Price with 21% gain on cost price: \[ S.P. = C.P. + 21\% \text{ of } C.P. = 100 + 21 = ₹121 \]Step 5: Equate the two expressions for S.P.: \[ \frac{22}{25} x = 121 \]Step 6: Solve for \(x\): \[ x = \frac{121 × 25}{22} = \frac{3025}{22} ≈ 137.5 \]Step 7: Marked price is above cost price by: \[ 137.5 – 100 = 37.5\% \]Answer: The marked price is 37.5% above the cost price.

Q12: Find a single discount equivalent to two successive discounts of 20% and 10%.

Step 1: Let the marked price be ₹100 (assumed).
Step 2: After first discount of 20%, price becomes: \[ 100 – 20\% \text{ of } 100 = 100 – 20 = ₹80 \]Step 3: After second discount of 10%, price becomes: \[ 80 – 10\% \text{ of } 80 = 80 – 8 = ₹72 \]Step 4: Single discount equivalent means: \[ 100 – \text{Single Discount} = 72 \\ \text{Single Discount} = 100 – 72 = 28\% \]Answer: The single discount equivalent to successive discounts of 20% and 10% is 28%.

Q13: Find a single discount equivalent to two successive discounts of 40% and 5%.

Step 1: Let the marked price be ₹100 (assumed).
Step 2: After first discount of 40%, price becomes: \[ 100 – 40\% \text{ of } 100 = 100 – 40 = ₹60 \]Step 3: After second discount of 5%, price becomes: \[ 60 – 5\% \text{ of } 60 = 60 – 3 = ₹57 \]Step 4: Single discount equivalent means: \[ 100 – \text{Single Discount} = 57 \\ \text{Single Discount} = 100 – 57 = 43\% \]Answer: The single discount equivalent to successive discounts of 40% and 5% is 43%.

Q14: Find a single discount equivalent to three successive discounts of 20%, 5% and 1%.

Step 1: Let the marked price be ₹100 (assumed).
Step 2: After first discount of 20%, price becomes: \[ 100 – 20\% \text{ of } 100 = 100 – 20 = ₹80 \]Step 3: After second discount of 5%, price becomes: \[ 80 – 5\% \text{ of } 80 = 80 – 4 = ₹76 \]Step 4: After third discount of 1%, price becomes: \[ 76 – 1\% \text{ of } 76 = 76 – 0.76 = ₹75.24 \]Step 5: Single discount equivalent means: \[ 100 – \text{Single Discount} = 75.24 \\ \text{Single Discount} = 100 – 75.24 = 24.76\% \]Answer: The single discount equivalent to successive discounts of 20%, 5% and 1% is approximately 24.76%.

Q15: The marked price of a watch is ₹1375. If tax is charged at the rate of 4%, find the total cost of the watch.

Step 1: Given,
Marked Price (M.P.) = ₹1375
Tax Rate = 4%
Step 2: Calculate tax amount: \[ \text{Tax} = \frac{4}{100} × 1375 = ₹55 \]Step 3: Total cost = Marked Price + Tax \[ = 1375 + 55 = ₹1430 \]Answer: The total cost of the watch including tax is ₹1430.

Q16: Ravi buys a bicycle with a marked price of ₹12500. He gets a rebate of 10% on it. After getting the rebate, tax is charged at the rate of 6%. Find the amount he will have to pay for a bicycle.

Step 1: Given,
Marked Price (M.P.) = ₹12500
Rebate = 10%
Tax Rate = 6%
Step 2: Calculate price after rebate: \[ \text{Price after rebate} = 12500 – \frac{10}{100} × 12500 = 12500 – 1250 = ₹11250 \]Step 3: Calculate tax on price after rebate: \[ \text{Tax} = \frac{6}{100} × 11250 = ₹675 \]Step 4: Total amount to be paid: \[ = 11250 + 675 = ₹11925 \]Answer: Ravi has to pay ₹11925 for the bicycle.

Q17: The list price of washing machine is ₹25000 and the shopkeeper gives a discount of 12% on the list price. On the remaining amount, he charges a tax of 10%. Find:

i. the amount of tax, a customer has to pay

Step 1: Given,
List Price (L.P.) = ₹25000
Discount = 12%
Tax Rate = 10%
Step 2: Calculate price after discount: \[ \text{Price after discount} = 25000 – \frac{12}{100} × 25000 = 25000 – 3000 = ₹22000 \]Step 3: Calculate tax on discounted price: \[ \text{Tax} = \frac{10}{100} × 22000 = ₹2200 \]Answer: The amount of tax the customer has to pay is ₹2200.

ii. the final price he has to pay for the washing machine

Step 4: Final price = Price after discount + Tax \[ = 22000 + 2200 = ₹24200 \]Answer: The final price the customer has to pay is ₹24200.

Q18: Reena pucharsed a face cream for ₹113.40 including tax. If the printed price of the face cream is ₹105, find the rate of tax on it.

Step 1: Given,
Printed Price (P) = ₹105
Price including tax = ₹113.40
Step 2: Let the rate of tax be \(r\%\).
Step 3: Price including tax formula: \[ P + \text{Tax} = P + \frac{r}{100} × P = P \left(1 + \frac{r}{100}\right) \] Given price including tax = ₹113.40, so: \[ 105 \left(1 + \frac{r}{100}\right) = 113.40 \]Step 4: Solve for \(r\): \[ 1 + \frac{r}{100} = \frac{113.40}{105} = 1.08 \\ \frac{r}{100} = 1.08 – 1 = 0.08 \\ r = 0.08 × 100 = 8\% \]Answer: The rate of tax on the face cream is 8%.

Q19: Vivek purchased a laptop for ₹34164, which includes 10% rebate on the marked price and then tax on the remaining price. Find the marked price of the laptop.

Step 1: Let Marked Price = ₹x.
Step 2: After 10% rebate, price becomes: \[ \text{Price after rebate} = x – \frac{10}{100} × x = \frac{90}{100}x = \frac{9}{10}x \]Step 3: After 4% tax on the price after rebate: \[ \text{Final Price} = \frac{9}{10} x + \frac{4}{100} × \frac{9}{10} x = \frac{9}{10} x \left(1 + \frac{4}{100}\right) = \frac{9}{10} x × \frac{104}{100} = \frac{936}{1000} x = \frac{117}{125} x \]Step 4: Given final price = ₹34164, so: \[ \frac{117}{125} x = 34164 \]Step 5: Solve for \(x\): \[ x = \frac{34164 × 125}{117} = \frac{4,270,500}{117} ≈ 36500 \]Answer: The marked price of the laptop is approximately ₹36,500.

Q20: Tanya buys an electric iron for ₹712.80. which includes two successive discount of 10% and 4% respectively on the marked price and then 10% tax on the remaining price. Find the marked price of the electric iron.

Step 1: Let Marked Price = ₹x.
Step 2: Price after first discount of 10%: \[ x_1 = x – \frac{10}{100} × x = \frac{90}{100} x = \frac{9}{10} x \]Step 3: Price after second discount of 4% on \(x_1\): \[ x_2 = x_1 – \frac{4}{100} × x_1 = \frac{96}{100} x_1 = \frac{96}{100} × \frac{9}{10} x = \frac{864}{1000} x = \frac{216}{250} x \]Step 4: After 10% tax on the discounted price \(x_2\): \[ \text{Final Price} = x_2 + \frac{10}{100} × x_2 = x_2 \times \left(1 + \frac{10}{100}\right) = x_2 × \frac{110}{100} = \frac{216}{250} x × \frac{110}{100} = \frac{216 × 110}{250 × 100} x = \frac{23760}{25000} x = \frac{594}{625} x \]Step 5: Given final price = ₹712.80: \[ \frac{594}{625} x = 712.80 \]Step 6: Solve for \(x\): \[ x = \frac{712.80 × 625}{594} = \frac{445500}{594} ≈ 750 \]Answer: The marked price of the electric iron is approximately ₹750.

Q21: Then price of a food processor inclusive of tax of 5% is ₹6930. If the tax is increased to 8%, how much more does the customer pay for it?

Step 1: Given,
Price including 5% tax = ₹6930
Tax rate 1 = 5%
Tax rate 2 = 8%
Step 2: Find the price before tax (base price): \[ \text{Base Price} = \frac{6930}{1 + \frac{5}{100}} = \frac{6930}{1.05} = ₹6600 \]Step 3: Calculate new price including 8% tax: \[ \text{New Price} = 6600 × \left(1 + \frac{8}{100}\right) = 6600 × 1.08 = ₹7128 \]Step 4: Calculate extra amount paid: \[ 7128 – 6930 = ₹198 \]Answer: The customer pays ₹198 more when tax increases from 5% to 8%.

Q22: The price of a laser printer including 7% tax, is ₹17384. How much less does a customer pay for it, if the tax on it is reduced to 4%?

Step 1:Let the cost excluding tax be \(x\).
Step 2:To find the base price (x):
\(x+(7/100)x=17334\)
\(x = 16200\)
Step 3:Now, calculate the price with 4% tax:
New price = \(x + (\frac{4}{100} \times x)\)
New price = \(16200 + (0.04 \times 16200) = 16200 + 648 = ₹16848\)
Step 4:Find the difference between the old and new price:
Saved amount = 17334 – 16848 = ₹486
Answer: The customer pays ₹486 less if the tax is reduced to 4%.