Subject: Compulsory Mathematics

Profit may refer to the difference between purchase price and cost price of bringing to market. Loss can be define as the act of losing.The seller may deduct a certain amount from the price of goods. The deduction is known as discount. The price from which the discount is deducted is called the marked price or labelled price. Value Added Tax is a tax imposed by the government based on goods and services in each step of production and distribution.

Amrit bought an article for Rs. 2,200 and sold it for Rs. 2,500. Here, his selling price is greater than the cost price. Hence, he got a profit of Rs. 2,500 - Rs. 2,200 = Rs. 300. If he had sold the article for Rs. 2000, he would have a loss of Rs. 2,200 - Rs. 2,000 = Rs. 200. The price for which an article is bought is known as the cost price (C.P.). The price for which it is sold is known as selling price (S.P.). If the selling price is greater than cost price, there is profit or gain. On the other hand, if the selling price is less than the cost price, there is a loss.

So, Profit = Selling price (S.P) - Cost price (C.P)

P = SP - CP and Loss =Cost price (C.P) -Selling price (S.P)

L = CP - SP

The percentage profit or loss can be calculated using the following formula.

Actual profit = profit% of cost price

\(\text {Profit percentage} = \frac {Profit} {C.P}\times 100\)

Actual loss = loss% of Cost price.

\(\text {Loss percentage} = \frac {Loss} {C.P}\times 100\)

If S.P and profit or loss percent are given then

\(C.P = \frac {S.P \times 100} {100 + P\%} \: {or}\: C.P = \frac {S.P \times 100} {100 - L\%}\)

If C.P. and profit or loss percentage are given then

\(S.P = \frac {C.P \times (100 + P\%)} {100}\: {or}\: S.P = \frac {C.P \times (100 - L\%)} {100}\)

The seller may deduct a certain amount from the price of goods. The deduction is known as discount. The price from which the discount is deducted is called the marked price or labeled price. The price obtained by deducting the discount from marked price is called selling price

i.e. Selling price (S.P) = Market price (M.P) - Discount

S.P = M.P - D

or, M.P = S.P + D

or, D = M.P - S.P

If there is no discount, selling price = marked price [ S.P = M.P ]

\(\text {Discount percentage} = \frac {Discount} {M.P} ×100%\)

Value Added Tax is a tax imposed by the government based on goods and services in each step of production and distribution. VAT is levied in the amount after allowing the discount (if there is) from the market price. In general, VAT is expressed in terms percentage which is called the rate of the VAT and it is fixed by the government. The cost of goods is determined by adding the VAT.

S.P = Orginal cost + VAT

\(\text {Rate of VAT} = \frac {VAT \;Amount} {Cost \; after \; discount (S.P)} \times 100\%\)

VAT amount = Rate of VAT (in%) \(\times\) discounted price.

- Profit or Gain = Selling Price - Cost Price

P = S.P - C.P - Profit percentage = \(\frac {Profit}{C.P} \times 100 \)
- Loss = Cost price - Selling Price

L = C.P - S.P - Loss percentage = \(\frac {Loss}{C.P} \times 100 \)
- Cost of goods or selling price = original cost + VAT
- Rate of VAT = \(\frac{VAT\; amount}{cost\; after\; discount\; (S.P)}\) \(\times\) 100%
- Vat Amount = Rate of VAT \(\times\) Discount price.
- The cost price of an article is constant.
- VAT is levied on discounted price.

- It includes every relationship which established among the people.
- There can be more than one community in a society. Community smaller than society.
- It is a network of social relationships which cannot see or touched.
- common interests and common objectives are not necessary for society.

By selling a radio with 25% profit, the profit amount is Rs 60 for how much price was it sold?

**Solution:**

Profit% = 12 %

Profit = Rs 60

Selling price (SP) =?

If profit Rs 12 then SP is Rs 112

If profit Rs 1 then SP is Rs \(\frac{112}{12}\)

If profit Rs 60 then SP is \(\frac{112}{12} \times 60 = Rs \: 560\)

\(\therefore SP\) = Rs 560_{Ans.}

If a carpet that cost Rs 4500 is sold at a profit of 30%, what is the selling price ?

**Solution:**

Cost price (CP) = Rs 4500

Profit % (P) = 30%

Selling price (SP) =?

\begin{align*} SP &= \left( \frac{100 + P%}{100} \right) \times CP \\ &= \frac{100 + 30}{100} \times 4500 \\ &= \frac{4500 \times 130}{100}\\ &= Rs \: 5850\end{align*}

\(\therefore SP\) = 5850_{Ans.}

A watch was bought for Rs 3405.50. At what price should it be sold to gain Rs 120.

**Solution:**

Cost price (CP) = Rs 3405.50

Gain (G) = Rs 120

Selling price (SP) = ?

We know that,

\begin{align*} SP &= CP + profit \\ &= Rs 3405.0 + Rs 120 \\ &= Rs 3525.50_{ANS.} \end{align*}

Bijay bought an old house for Rs 220,000 and spend Rs 83,500 for its repair and decoration. If he sold the house for Rs 300,000 find his loss percentage.

**Solution:**

Cost price (CP) = Rs 220,000 + Rs 83500 = Rs 303,500

Selling price (SP) = Rs 300,000

Loss% =?

\begin{align*} Loss\% &= \frac {CP -SP} {CP} \times 100\% \\ &= \frac{303,500 - 300,000}{303500} \times 100\% \\ &= 1.15\% \end{align*}

\(\therefore \) Loss = 1.15%_{Ans.}

A radio is sold for Rs 2700, there is a loss of 10% at what price should it be sold to gain \( 7 \frac{1}{2}\%.\)

**Solution:**

Selling price (SP) = Rs 2700

Loss% = 10%

\begin{align*} Cost \: price (CP) &= \frac{SP \times 100}{100 - L\%} \\ &= \frac {2700 \times 100}{100 - 10 }\\ &= \frac{270000}{90} \\ &= Rs \: 3000 \end{align*}

Again,

CP = Rs 3000

Profit % = 7.5%

SP = ?

\begin{align*} SP &= \frac{1100 + P\%}{100 } \times CP \\ &= \frac{100 + 7.5\times 3000}{100}\\ &= Rs \: 3225 \end{align*}

\( \therefore \) selling price = 3325_{Ans}

What percent of discount should be given in a doll costing Rs. 180 such that a customer has to buy it for Rs 160?

**Solution:**

The price of doll before discount = Rs 180

The price of doll after discount = Rs 160

Amount of discount = Rs 180 - Rs 160 = Rs 20

\begin{align*} Discount \% &= \frac{Amount \: of \: discount }{Initial \: price} \times 100\% \\ &= \frac{20}{180} \times 100\% \\ &= 11.11\% _{Ans.} \end{align*}

At 18% loss the selling price of an articles is Rs 164. Calculate the cost price of the article.

**Solution:**

Selling price (SP) = Rs. 164

Loss = 18%

\begin{align*} Cost \: price (C.P.) &= \frac{S.P. \times 100}{100 - Loss \%} \\ &= \frac{164 \times 100}{100 - 18}\\ &= \frac{16400}{82}\\ &= Rs. 200 _{Ans}\end{align*}

How much should you have to pay to buy the volleyball shown in the figure?

**Solution:**

Market price (MP) = Rs. 1000

Discount % = 10%

\begin{align*}Payment\: amount &= MP - discount\% of MP \\ &= Rs. \: 1000 - \frac{10}{100}\times 1000\\ &= Rs. 1000 - Rs. 100 \\ &= Rs. 900_{Ans} \end{align*}

What percentage of discount should be given in a doll costing Rs 150 so that a customer can purchase it at Rs 130? Find it.

**Solution:**

Marked price (MP) = Rs. 150

Selling price after discount (SP) = Rs. 130

\begin{align*} Discount\% &= \frac{MP - SP}{MP} \times 100\% \\&= \frac {150 - 130}{150} \times 100\% \\ &= 13\frac{1}{3} \% \: \: _{Ans}\end{align*}

A watch was bought for Rs 1200. At what labelled price should it be sold to gain \(33\frac{1}{3}\%\) after discount 20% . Find also its selling price.

**Solution:**

Cost price of watch (CP) = Rs 1200

Let, marked price (MP) = Rs x

Discount = 20%

\begin{align*} Selling \: price \: (SP) &= MP - MP \: of \: discount\% \\ or, SP &= Rs \: x - Rs\: x \times \frac{20}{100} \\ SP &= Rs\: \frac{5x -x}{5}\\ &= Rs \: \frac{4x}{5} \end{align*}

\begin{align*} Profit &= Rs \: 1200\: of \: \frac{100}{3}\% \\ &= Rs \: 1200\: \times \: \frac{100}{3} \times \frac {1}{100} \\ &= Rs. \: 400 \end{align*}

We know that,

\begin{align*} SP &= CP + Profit \\ or, \frac{4x}{5} &= Rs \: 12000 + Rs. \: 4000 \\ or, x &= Rs \frac{1600 \times 5}{4} \\ &= Rs. 2000 \end{align*}

\(\therefore\) Labbled price of watch = Rs 2000

\(\therefore\) SP = 1200 + 400 = Rs 1600 _{Ans}

A shopkeeper marks the price of an article 40% above the cost price. After allowing a discount of 15% on its marked price, It was sold at a gain of Rs 950. Find the marked price of the article.

**Solution:**

Cost price of television (CP) = Rs x

\begin{align*}Marked \: price\: (MP) &= x + x\: of \:40\%\\ &= x + x \times \frac{40}{100} \\ &= \frac{5x + 2x}{5}\\ &= \frac{7x}{5} \end{align*}

Discount = 15%

\begin{align*}Selling \: price (SP) &=MP - MP \times Discount\% \\ &= \frac{7x}{5} - \frac{7x}{5} \times \frac{15}{100} \\ &= \frac {7x}{5} - \frac{21x}{100} \\ &= Rs \: \frac{140x - 21x}{100} \\ &= Rs \: \frac{119x}{100} \end{align*}

Profit = Rs 950

We know that,

\begin{align*} Profit &= SP - CP\\ or, 950 &= \frac{119x}{100} - x \\ or, 950 &= \frac{119x -100x}{100} \\ or, \frac{19x}{100} &= 950\\ or, x &= \frac{950 \times 100}{19}\\ &= Rs 5000 \end{align*}

The cost price = Rs 5000

Marked price (MP) = \( \frac{7 \times 5000}{5} = Rs \: 7000 \: \: _{Ans}\)

When a discount of 15% is allowed on the marked price of an article, It is sold for Rs 4250. Calculate the marked price. If the marked price is 25% above the cost price of the article. Calculate the gain or loss percent.

**Solution:**

Let, marked price (MP) = Rs x

Selling price (SP) = Rs 4250

Discount = 15%

\begin{align*} SP &= MP - MP \: of\: discount\% \\ 4250 &= x -x \times \frac{15}{100}\\ or, 4250 &= \frac{20x - 3x}{20} \\ or, 4250 &= \frac{17x}{20}\\ or, x &= \frac{4250 \times 20}{17}\\ &= Rs. \: 5000 \end{align*}

Again, Let CP = Rs y

\begin{align*} MP &= CP + CP \: of \: 25\% \\ or, MP &= y + y \times \frac{25}{100} \\ or, MP &= \frac{4y + y}{4} \\ or, MP &= \frac{5y}{4}\\ or, \frac{5y}{4} &= 5000 \\ or, y &= \frac{5000 \times 4}{5}\\ &= 4000 \end{align*}

SP = Rs 4250

CP = Rs 4000

\begin{align*} Profit\% &= \frac{SP - CP}{CP} \times 100\% \\ &= \frac{4250 - 4000}{4000} \times 100\% \\ &= \frac{250}{40}\% \\ \therefore profit \: percentage &= 6.25\% \end{align*}

Find the total selling price of a shirt whose marked price is Rs 2700 when 13% VAT is levied?

**Solution:**

Marked price (P) = Rs 2700

VAT = 13%

\begin{align*} Selling \: price \: (SP) &= MP + VAT\% of MP\\ &= 2700 + \frac{13}{100} \times 2700 \\ &= 2700 + 351 \\ &= Rs. \: 3051 \: \: \: _{Ans.} \end{align*}

A shopkeeper gained Rs 8 by selling a pen allowing 10% discount. He would have gained Rs 20. If discount was not allowed. What was the selling price?

**Solution:**

Let, marked price (MP) = Rs x, discount = 10%

\begin{align*} SP &= MP - MP \: of \: discount\% \\ &= x - x \times \frac{10}{100} \\ &= \frac{10x - x}{10}\\ &= \frac{9x}{10} \end{align*}

\begin{align*} CP_1 &= SP - Profit\\ &= \frac{9x}{10} - 8 \end{align*}

Again, MP = SP = Rs x

Profit = Rs 20

\( CP_2 = SP - profit = x - 20 \)

Now,

\begin{align*} CP_1 &= CP_2 \\ or, \frac{9x}{10} - 8 &= x - 20 \\ or, \frac{9x - x}{x} &= 8 - 20\\ or, \frac{9x - 10x}{10} &= -12\\ or, -x &= -120 \\ \therefore x &= 120 \\ \text{Putting the value of x in SP } = \frac{9x}{10}\\ SP &= \frac{9 \times 120}{10}\\ &= Rs\: 108\\ \therefore Selling \: price = Rs\: 108_{Ans} \end{align*}

Reetu sold a watch to Reshmi at 20% profit. Reshmi again sold the same watch to Dikita for Rs 1350 at loss of 10%. At what price did Reetu purchase the watch?

**Solution:**

For Reshmi

Selling price (SP) = Rs 1350

Loss % = 10%

\begin{align*} CP &= \frac{100 \times SP}{100 - L\%} \\ &= \frac{100 \times 1350}{100 - 10}\\ &= \frac{135000}{90}\\ &=Rs \: 1500 \end{align*}

Reshmi cost price is selling price of Reetu

For Reetu

SP = Rs 1500

Profit % = 20 %

\begin{align*} CP &= \frac{100 \times SP}{100 + P\%} \\ &= \frac{100 \times 1500}{100 + 20}\\ &= \frac{150000}{120}\\ &= Rs \: 1250\end{align*}

\( \therefore \)The cost price = Rs 1250

A dishonest shopkeeper has the false weights one kind of weight 20% more while buying goods and the other weight 20% less while selling the goods. Find his gain percent just by weighting?

**Solution:**

Let, the weight 100 gain while buying the goods. The actual weight of the purchasing goods = 120 gram. Let weights 120 gram while selling the goods but the actual weight of the selling goods = 100 gram.

Let the CP of 1 gram of goods = Rs 1

the CP of 100 gram of goods = Rs 100 x

the CP of 120 gram of goods = Rs 120 x

He sells the goods of costing Rs 100x for Rs 120x

He sells the goods of costing 1 for \( \frac{120x}{100x} \)

He sells the goods of costing 120x for \( \frac{120x}{100x} \times 120x = Rs \: 144x \)

SP of goods = Rs 144x

CP of goods = Rs 100x

\begin{align*} Profit \: \% &= \frac{SP - CP}{CP} \times 100\% \\ &= \frac{144x - 100x}{100x} \times 100\% \\ &= 44\% \end{align*}

\(\therefore\) Profit = 44%

When a cycle is sold allowing 10% discount on its marked price a seller gains 5% and allowing 5% discount profit is Rs 338. Find the cost price of the cycle.

**Solution:**

Let, MP = Rs x, discount = 10%

\begin{align*} SP &= MP - MP \: of \: discount\% \\ &= x -x \times \frac{10}{100}\\ &= x - \frac{x}{10}\\ &= \frac{10x - x}{10}\\ &= Rs \frac{9x}{10} \end{align*}

Profit = 5%

\begin{align*} CP &= \frac{SP \times 100}{100 + P%} \\ &= \frac{\frac{9x}{10} \times 100}{100 + 5}\\ &= \frac{90x}{105}\\ &= \frac{6x}{7}\: \: \: \: \: \: \: .........(i) \end{align*}

Again,

\begin{align*} SP &= x - x\: of \: 5\% \\ &= x -x \times \frac{5}{100}\\ &= x - \frac{x}{20}\\ &= \frac{20x - x}{20}\\ &= Rs \: \frac{10x}{20} \end{align*}

Profit = Rs 338

\(CP = SP - Profit \: = \frac{19x}{20} - 338 \: \: \: \: \: \: \: \: \: \: ......(ii)\)

From eq^{n}(i) and eq^{n} (ii)

\begin{align*} \frac{19x}{20} - 338 &= \frac{6x}{7} \\ or, \frac{19x}{20} - \frac{6x}{7} &= 338\\or, \frac{113x - 120x}{140} &= 338\\or, 13x &= 388 \times 140\\ or, x &= \frac{47320}{13}\\ x &= Rs \: 3650\end{align*}

Putting value of x in eq^{n} (i)

\begin{align*} CP &= \frac{6x}{7} \\&= \frac{6 \times 3640}{7}\\ \therefore CP &= Rs \: 3120\end{align*}

Ritu bought a watch and calculator for Rs 4000. If she sold a watch at 10% profit and calculator at 20% loss, then she gets only 1% profit in whole. Find the cost price of the calculator and the watch.

**Solution:**

Let, cost price of calculator (CP_{1}) = Rs x

Cost price of the watch (CP_{2}) = RS (4000 - x)

\begin{align*} SP \: of \: calculator \: (SP_1) &= CP + profit \\ &= x + x \: of \: 10\% \\ &= x + x \times \frac{10}{100}\\ &= \frac{11x}{10}\end{align*}

\begin{align*}SP \: of\: watch \: (SP_2) &=CP - loss\\ &= (4000 - x) -20\% \: of \: (4000 + x)\\ &= (4000 -x) - \frac{20}{100} \times (4000 - x)\\ &=\frac{32000 - 5x -4000 + x}{5}\\ &= 3200 - \frac{4x}{5} \end{align*}

\begin{align*} Total \: SP &= SP_1 + SP_2 \\ &= \frac{11x}{10} + 3200 - \frac{4x}{5}\\ &= \frac{3x}{10} + 3200 \end{align*}

Total CP = 4000

Profit = 1%

\begin{align*}SP &= CP + Profit\\ or, \frac{3x}{10} + 3200 &= 4000 + 1\% of 4000\\ or, \frac{3x}{10} + 3200 &= 4000 + \frac{1}{100} \times 4000\\ or, \frac{3x}{10} &= 4000 + 40 - 3200\\ x &= 840 \times \frac{10}{3}\\ &= Rs \: 2800 \end{align*}

\begin{align*}\text{CP of watch = Rs} \: 4000 -x \\ &= 4000 - 2800 \\ &= 1200 \end{align*}

\( \therefore \) CP of calculator = Rs 2800

\(\therefore\) CP of watch = Rs 1200_{Ans.}

When a article was sold with 10% discount there was a loss of Rs 100. If it was sold with 5% discount there would have been Rs 100 profit. Find the cost price and the market price of an article.

**Solution:**

Let, MP = Rs x

Loss = Rs 100

Discount = 10%

\begin{align*} SP &= MP - MP \: of\: discount \\ or, SP &= x - x \times \frac{10}{100} \\ \frac{10x - x}{10}\\ &= Rs \: \frac{9x}{10} \end{align*}

CP_{1} = SP + Loss = \( \frac{9x}{10} + 100 \: \: \: \: .......(i)\)

Again,

discount = 5%

Profit = Rs 100

\begin{align*} SP &= MP - MP \: of \: discount\% \\ &= x -x \times \frac{5}{100}\\ &= x - \frac{x}{20}\\ &= \frac{20x - x}{20} \\ \therefore SP &= Rs \: \frac{19x}{20} \\Now, \\ CP_2 &= SP - Profit \\ CP &= \frac{19x}{20} - 100 \: \: \: \: \: .......(ii) \end{align*}

From equation (i) and (ii)

\begin{align*}\frac{9x}{10} + 100 &= \frac{19x}{20} - 100 \\ or, \frac{19x}{20} - \frac{9x}{10} &= 100 + 100\\ or, \frac{19x - 18x}{20}&= 200 \\ or, x &= Rs \: 4000 \end{align*}

Marked price = Rs 4000

\begin{align*} CP &= \frac{9x}{10} + 100 \\ &= \frac{ 9 \times 4000}{10} + 100\\ &= 3600 + 100\\ &= Rs \: 3700_{Ans}\end{align*}

An article when sold at a profit of 5% yields Rs 15 more than when sold at loss of 5%, what was its cost price?

**Solution:**

Let, CP = Rs x

Loss % = 5%

\begin{align*} SP_1 &= CP - CP \: of \: loss\%\\ &= x - x \times \frac{5}{100} \\ &= \frac{20x - x}{20} \\ &= Rs \: \frac{19x}{20} \end{align*}

If he charge Rs 15 more

\( SP_2 = Rs \: \frac{19x}{20} + 15\)

We know that,

\begin{align*} CP + Profit &= SP_2\\ or, x + x \times \frac{5}{100}&= \frac{19x}{20} + 15 \\ or, \frac{20x + x}{20} &= \frac{19x + 300}{20}\\ or, 21x - 19x &= 300\\ or, 2x &= 300\\ or, x &= \frac{300}{2}\\ &= Rs \: 150 \end{align*}

\(\therefore\) The cost price = Rs 150_{Ans.}

A man bought a radio sets for Rs 500. He sold one at a loss 12% and the other at a gain of 8%. He neither gained nor loss in his transaction. Find the cost price of each radio.

**Solution:**

Let, cost price of 1^{st} radio (CP_{1}) = Rs x

Loss % = 12%

Selling price of 1^{st} radio (SP_{1}) = ?

\begin{align*} SP_1 &= \frac{100 - L\%}{100} \times CP_1 \\ &= \frac{100 - 12}{100} \times x \\ &= \frac{88x}{100}\\ &= Rs \: \frac{22x}{25} \end{align*}

Let cost price of 2^{nd}radio (CP_{2}) = Rs 500 - x

Profit % (P%) = 8%

Selling price of 2_{nd}radio (SP_{2}) = ?

\begin{align*} SP_2 &= \frac{100 + P\%}{100} \times CP_2 \\ &= \frac{100 + 8}{100} \times( 500 - x) \\ &= \frac{108 \times (500 - x)}{100}\\ &= Rs \: \frac{27 (500 - x)}{25} \end{align*}

From question,

\begin{align*} \frac{22x}{25} + \frac{27(500 - x)}{25} &= 500\\ or, \frac{22x + 13500 - 27x}{25} &= 500 \\ or, 13500 - 5x &= 12500 \\ or, 5x &= 13500 - 12500\\ or, x &= \frac{1000}{5} \\ \therefore x &= Rs \: 200 \end{align*}

Cost price of 1^{st} radio = Rs 200

Cost price of 2^{nd} radio = Rs 500 - x = 500 - 200 = Rs 300_{Ans.}

Find the rate of discount. If a telephone set price Rs 1350 is sold for Rs 1282.50.

**Solution:**

Marked price (MP) = Rs 1350

Selling Price (SP) = Rs 1282.50

\begin{align*} Discount &= MP -SP \\&= 1350 - 1282.50 \\ &= Rs \: 67.50 \end{align*}

\begin{align*} Discount\% &= \frac{Discount}{MP} \times 100\% \\ &= \frac{67.50}{1350} \times 100 \\ &= 5\% \: \: _{Ans.} \end{align*}

What is the value of VAT by 10% of computer of selling price is Rs 29660?

**Solution:**

Selling price (SP) = Rs 29660

VAT % = 10 %

\begin{align*} \text {Amount of VAT} &= 29660 \times \frac{10}{100} \\ &= Rs \: 2966 \end{align*}

VAT at 10% of the original price is charge on Jewelry of gold. How much VAT was paid if the value included VAT is Rs 17050?

**Solution:**

Let, MP = Rs x,

VAT = 10%

\begin{align*} x + x \: of \: 10\% &= 17050 \\ or, x + x \times \frac{10}{100} &= 17050 \\ or, \frac{10x + x}{10} &= 17050 \\ or, x &= \frac{17050 \times 10}{11} \\ \therefore x &= Rs \: 15500 \end{align*}

\begin{align*} \text{Amount of VAT } &= Rs 17050 - Rs 15500 \\ &= Rs 1550 \: _{Ans.} \end{align*}

A tourist buys 5 set of Nepali dress at RS 650 per set. If VAT rate is 10% how much will receive while leaving Nepal?

**Solution:**

Let, cost price (CP) = Rs x

VAT = 10%

\begin{align*} x + x \: of \: 10\% &= 650 \\ or, x + x \times \frac{10}{100} &= 650\\ or, \frac{11x}{10} &= 650 \\ or, x &= \frac{650 \times 10}{11}\\ \therefore x &= Rs \: 590.90 \end{align*}

Return money for 1 set = Rs 650 - Rs 590.90 = Rs 59.10

Return money for 5 sets = 5 \(\times\) 59.10 = Rs 295.50

Price of a TV is Rs 24,000. If the price is discounted by Rs 1200. What is the discount percentage?

**Solution:**

Price of TV = Rs 24,000

Amount of discount = Rs 1200

Discount % = ?

\begin{align*} Discount\% &= \frac{Discount \: Amount}{Price \: of \: TV} \times 100\% \\ &= \frac{1200}{24000} \times 100\%\\ &= 5\% \end{align*}

\(\therefore \) Discount = 5%

The marked price of a calculator is Rs 260. What is the sale price of it, If 5% discount is allowed?

**Solution:**

Marked price (MP) = Rs 260

Discount % = 5%

Selling price (SP) = ?

\begin{align*} SP &=MP - MP \: of \: discount\% \\ &= 260 - 260 \times \frac{5}{100} \\ &= Rs \:260 -13 \\&= Rs \: 247 \end{align*}

\(\therefore \) SP = Rs 247 \(_{Ans}\)

The price of an article with 15% VAT is Rs 690. What will be the price excluding VAT?

**Solution:**

Let marked price (MP) = Rs x

The price of the article with VAT = Rs 690

VAT =15%

We know that,

The price of the article with \begin{align*} VAT &= x + x \: of \: 15\% \\ 690 &= x + x \times \frac{15}{100} \\ or, 690 &= \frac{23x}{20}\\ or,x &= \frac{690 \times 20}{23} \\ x &= Rs \: 600 \end{align*}

The price excluding VAT is Rs 600.

An article with marked price Rs 80,000 is sold allowing a discount of 5%, what is the price after discount?

**Solution:**

Marked price (MP) = Rs 80,000

Discount = 5%

\begin{align*}Selling\: price \:(SP) &= MP - MP \: of \: discount\% \\ &= Rs 80000 - 80000 \times \frac{5}{100}\\ &= Rs \: 80,000 - 4000 \\&= Rs \: 76,ooo \: \: _{Ans.} \: \end{align*}

The price of computer inclusive the VAT at 15% is Rs 46,000. Find its price exclusive of the VAT.

**Solution:**

The price of computer before VAT = Rs x, VAT = 15%

Cost of computer after adding VAT = Rs 46000

\begin{align*} x + x \: of \: 15 &= Rs \: 46000\\ or, x + x \times \frac{15}{100} &= Rs \: 46000\\ or, \frac{20x + 3x}{20} &= 46000 \\ or, x &= \frac{46000 \times 20}{23}\\ \therefore x &= Rs \: 40,000 \end{align*}

\(\therefore \) The price of exclusive of the VAT = Rs 40,000 \(_{Ans.}\)

The marked price of a bicycle was Rs 5550. What will the price of the bicycle, if 15% VAT was levied allowing 10% discount unit?

**Solution**:

Marked price of a bicycle (MP) = Rs 5550

Discount = 10%

VAT = 15%

After discount,

\begin{align*} Selling \: price \: (SP_1) &= MP - Discount\% \: of \: MP\\ SP_1 &= Rs \: 5550 - 5550 \times \frac{10}{100} \\ &= 5550 - 555\\ &= Rs \: 4995 \end{align*}

After, adding VAT

\begin{align*} SP_2 &= SP_1 + VAT\% \:of\: SP_1 \\ &= 4995 + 4995 \times \frac{15}{100}\\ &= Rs \: 4995 + Rs \: 749.30 \\ &= Rs\: 5744.25 \: \: \: \: \: \: _{Ans.} \end{align*}

Allowing 20% discount on the marked price of a watch, the value of the watch will be Rs 2376. When a VAT of 10% is added.

**Solution:**

Let, marked price (MP) = Rs x

Discount = 20%

VAT = 10%

After discount,

\begin{align*} Selling \: price \: (SP_1) &= MP - Discount \% \: of \: MP\\ &= Rs \: x - x \times \frac{20}{100} \\ &= x - \frac{x}{5}\\ &= \frac{5x -x}{5}\\&= Rs \: \frac{4x}{5} \end{align*}

After adding VAT,

\begin{align*} SP_2 &= SP_1 + VAT\% \: of \: SP_1 \\ or, 2376 &= \frac{4x}{5} + \frac{4x}{5} \times \frac{10}{100}\\ or, 2376 &= \frac{40x + 4x}{50}\\ or, 2376 &= \frac{44x}{50} \\ or, x &= \frac{2376 \times 50}{44} \\ x &= Rs \: 2700 \end{align*}

\(\therefore \) the marked price = Rs 2700 \(_{Ans.}\)

If the marked price of camera is Rs 3200. A shopkeeper announces a discount of 8%. How much will a customer have to pay for buying the camera, If 10% VAT was levied on it?

**Solution:**

Marked price (MP) = Rs 3200

Discount = 8%

After discount,

\begin{align*}Selling \: price \: (SP_1)&= MP - MP\: of \: discount \% \\ &= 3200 - 256 \\ &= Rs \: 2944 \end{align*}

After adding VAT

\begin{align*}Selling \: price \: (SP_2) &= Sp_1 + SP_1 \: of \: VAT \% \\ &= 2944 + 2940 \times \frac{10}{100}\\ &= Rs \: 2944 + 294.40 \\ &= Rs \: 3238.40 \end{align*}

\(\therefore\) The customer pay for camera = Rs 3238.40 \(_{Ans}\)

After allowing 10% discount on he market price of television 15% VAT levied on it. Its price was fixed to be Rs 16720. What amount was given in discount?

**Solution:**

Let marked price (MP) = Rs x

Discount = 10%

VAT = 15%

After discount,

\begin{align*} Selling \: price\: (SP_2)&= MP - MP \: of \: discount\% \\ &= x - x \times \frac{x}{10}\\ &= \frac{10x - x}{10} \\ &= Rs \: \frac{9x}{10} \end{align*}

After adding VAT

\begin{align*} Selling \: price\: (SP_2) &= SP_1 + SP_1 \: of \: VAT\% \\ 1670 &= \frac{9x}{10} + \frac{9x}{10} \times \frac{15}{100} \\ or, 16750 &= \frac{9x}{10} + \frac{27x}{200}\\ or, 16720 &= \frac{180x + 27x}{200}\\ or, x &= \frac{16720 \times 200}{207} \\ &= Rs \: 16154.50 \end{align*}

\begin{align*} Amount \: of \: discount &= x \: of \: 10\% \\ &= 16154.50 \times \frac{10}{100}\\ &= Rs \: 1615.45 \end{align*}

If actual selling price of an including 20% discount and 10% VAT is Rs 880, find the market price of the article.

**Solution:**

Let, MP = Rs x

Discount = 20%

VAT = 10%

Amount of VAT = Rs 880

After discount,

\begin{align*}Selling\: price \: (SP_1) &= MP - discount\% \:of \: SP_1 \\ &= x - x \times \frac{20}{100}\\ &= x- \frac{x}{5}\\ &= \frac{5x -x}{5}\\ &= Rs \: \frac{4x}{5}\end{align*}

After adding VAT,

\begin{align*} Selling \: price \: (SP_2)&= SP_1 + VAT\% \:of\: SP_1\\ 880 &= \frac{4x}{5} \times \frac{10}{100}\\ or, 880 &= \frac{4x}{5} + \frac{2x}{25} \\ or, 880&= \frac{20x + 2x}{25}\\ or, 880 &= \frac{22x}{25}\\ or, x &= \frac{880 \times 25}{22}\\ &= Rs \: 1000 \end{align*}

\(\therefore\) Marked price = Rs 1000 \(_{Ans}\)

The marked price of a radio was Rs 5000. What will be price of the radio, If 10% VAT was levied after allowing 15% discount on it?

**Solution:**

Marked price (MP) = Rs 5000

Discount = 15%

VAT = 10%

\begin{align*} Selling \: price \: (SP_1) &= MP - MP \: of \: discount\% \\ &= 5000 - 5000 \times \frac{15}{100}\\ &= Rs \: 5000 - 750\\&= Rs \: 4250\end{align*}

After adding VAT

\begin{align*} Selling \: price \: (SP_2)&= SP_1 + SP_1 \: of\: VAT \\ &= 4250 + 4250 \times \frac {10}{100}\\ &= Rs \: 4250 + Rs \: 425 \\ &= Rs \: 4675 \end{align*}

\(\therefore\) The price of the radio = Rs 4675 \(_{Ans.}\)

After allowing 16% discount on the market price of an article and levying 13% value added tax, then the price of the article becomes to Rs 9,942. Find the value added tax.

**Solution:**

Let, Marked price = Rs x

\begin{align*}\text{The price after discount} &= x-x \times 16\%\\ &= x - x \times \frac{16}{100}\\ &= \frac{25x - 4x}{25}\\ &= \frac{21x}{25} \end{align*}

\begin{align*}\text{The price after VAT} &= \frac{21x}{25} + \frac{21x}{25} \times 13\% \\ or, 9492&= \frac{21x}{25 } \frac{21x}{25} \times \frac{13}{100} \\ or, 9492 &= \frac{21x}{25} + \frac{273x}{2500}\\ or, 9492 &= \frac{2100x + 273x}{2500}\\ or, 9492 \times 2500 &= 2373x\\ or, \frac{23730000}{2373} &= x\\ \therefore Market \: price\: (x) &= 1000 \end{align*}

\begin{align*} Amount \: of \: VAT &= \frac{21x}{25} \times \frac{13}{100} \\ &= \frac{21 \times 10000 \times 13}{25 \times 100}\\ &= Rs \: 1092\: \: _{Ans.}\end{align*}

A shopkeeper sold his goods for Rs 28815 allowing 15% discount and the levied 13% VAT. What was the amount of discount?

**Solution:**

Let, marked price (MP) = Rs x

Discount = 15%

VAT = 13%

After discount,

\begin{align*} Selling \: price \: (SP_1) &= MP - discount\%\: of\: MP\\ &= x -x \times \frac{15}{100}\\ &= x-\frac{3x}{10}\\ &= \frac{20x - 3x}{20}\\ &= \frac{17x}{20} \end{align*}

After adding VAT,

\begin{align*} Selling \: price \: (SP_2) &= SP_1 + VAT\% \: of \: (SP_1)\\ 28815 &= \frac{17x}{20} + \frac{17x}{20} \times \frac{13}{100}\\ or, 28815 &= \frac{17x}{20} + \frac{221x}{2000}\\ or, 28815 &= \frac{1921x}{2000}\\ or, x &= \frac{28815 \times 2000}{1921}\\ &= Rs \: 30,000 \end{align*}

\begin{align*} \text{Amount of discount} &= 30,000 \times \frac{15}{100}\\ &= Rs \: 4500 \: \: _{Ans.} \end{align*}

A tourist bought a Nepali blanket at 20% discount and 10% VAT. At the Airpot the tourist got Rs 440 back for the VAT. What was the marked price of the blanket ?

**Solution:**

Let, Marked price (MP) = Rs x

Discount = 20%

VAT = 10%

After discount

\begin{align*} Selling \: price \: (SP_1) &= MP - Discount\% \: of \: MP\\ &= x-x \times \frac{20}{100}\\ &= \frac{5x -x}{5} \\ &= Rs \frac{4x}{5} \end{align*}

\begin{align*} Amount\: of \:VAT &= VAT\:of\:SP_1 \\ 440 &= \frac{4x}{5} \times \frac{10}{100}\\ or, 440 &= \frac{2x}{25}\\ or, x &= \frac{440 \times 25}{2}\\ \therefore x &= Rs \: \: 5500 \end{align*}

\(\therefore\) Marked price of the blanket = Rs 5500 \(_{Ans.}\)

After allowing 20% discount on the marked price of computer, 15% VAT was levied on it. If its price became Rs 22080. What amount was levied in the VAT?

**Solution:**

Let, Marked price (MP) = Rs x

Discount = 20%

VAT = 15%

After discount

\begin{align*} Selling \: price \: (SP_1) &= MP - Discount\% \: of \: MP\\ &= x-x \times \frac{20}{100}\\ &= \frac{5x -x}{5} \\ &= Rs \frac{4x}{5} \end{align*}

After adding VAT

\begin{align*} Selling \: price\: (SP_2) &= SP_1 + VAT\% \: of \: SP_1 \\ 22080 &= Rs \: \frac{4x}{5} + \frac{4x}{5} \times \frac{15}{100}\\ or, 22080 &= Rs \: \frac{4x}{5} + \frac{12x}{100}\\ or, 22080 &= \frac{80x + 12x}{100}\\ or, 22080 &= \frac{92x}{100}\\ or, x &= \frac{22080 \times 100}{92} \\ x &= Rs \: 24000\end{align*}

Marked price = Rs 24000

\begin{align*} \text{Amount of VAT} &= Rs \: \frac{4x}{5} \times \frac{15}{100}\\ &= \frac{4 \times 24000 \times 5}{5 \times 100}\\ &= Rs \: 2880 \end{align*}

\(\therefore\) Amount of VAT = Rs 2880 \( \: \: _{Ans.}\)

The marked price of an article is 4000. If the price of the article including 13% VaT is Rs 3616, find the discount percentage given in it.

**Solution:**

The marked price (MP) = Rs 4000

The amount of discount = Rs x

The price of article after discount = Rs (4000 - x)

VAT % = 13 %

From question,

\begin{align*} (4000 - x) (4000 - x) \times \frac{13}{100} &= 3616 \\or, \frac{400000- 100x + 52000 - 13x}{100} &= 3616\\ or, 452000-113x &= 361600\\ or, 113x &= 452000 - 361600\\ or, x &= \frac{90400}{113}\\ \therefore x &= Rs. \: 800\end{align*}

\begin{align*} Percent \: discount &= \frac{Amount \: of \: discount}{MP} \times 100\% \\ &= \frac{800}{4000} \times 100\% \\ &= 20\% \: \: \: _{Ans.} \end{align*}

© 2019-20 Kullabs. All Rights Reserved.