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**Question 1.** A shop gives 20% discount. What would the sale price of each of these be?

(a) A dress marked at Rs 120 (b) A pair of shoes marked at Rs 750 (c) A bag marked at Rs 250

**Solution:**

**(a) **Marked price of the dress = Rs 120

Discount rate = 20%

∴ Discount = 20% of Rs 120

= Rs 20/100 * 120

= Rs 2 * 12 = Rs 24

∴ Sale price of the dress = [Marked price] – [Discount]

= Rs 120 – Rs 24

= Rs 96

**(b)** Marked price of the pair of shoes = Rs 750

Discount rate = 20%

∴ Discount = 20% of Rs 750

= Rs 20/100 * 750

= Rs 2 * 75 = Rs 150

Now,

Sale price of the pair of shoes = [Marked price] – [Discount]

= Rs 750 – Rs 150 = Rs 600

**(c) **Marked price of the bag = Rs 250

Discount rate = 20%

∴ Discount = 20% of Rs 250

= Rs 20/100 * 250

= Rs 2 * 25 = Rs 50

∴ Sale price of the bag = [Marked price] – [Discount]

= Rs 250 – Rs 50 = Rs 200

**Question 2. **A table marked at Rs 15,000 is available for Rs 14,400. Find the discount given and the discount per cent.

**Solution:**

Marked price of the table = Rs 15000

Sale price of the table = Rs 14400

∴ Discount = [Marked price] – [Sale price]

= [Rs 15000] – [Rs 14400]

= Rs 600

Discount per cent = Discount/Marked price x 100

= 600/15000 * 100%

= (2 * 2)%

= 4%

**Question 3.** An almirah is sold at Rs 5,225 after allowing a discount of 5%. Find its marked price.

**Solution:**

Sale price of the almirah = Rs 5225

Discount rate = 5%

Since, Discount = 5% of marked price

∴ [Marked price] – Discount = Sale price

or [Marked price] – 5/100 * [Marked price] = Sale price

or Marked price = Sale price

or Marked price 95/100 = Sale price (= Rs 5225)

or Marked price = Rs 5225 * 100/95

= Rs 5500

**Question 1.** Find selling price (SP) if a profit of 5% is made on

(a) a cycle of Rs 700 with Rs 50 as overhead charge.

(b) a lawn mower bought at Rs 1150 with Rs 50 as transportation charges.

(c) a fan bought for Rs 560 and expenses of Rs 40 made on its repairs.

**Solution:**

**(a)** ∵ Total cost price = Rs 700 + Rs 50 (Overhead expenses)

= Rs 750

Profit = 5% of Rs 750

= Rs 5/100 * Rs 750 = Rs 5 * 15/2

= Rs 75/2 = Rs 37.50

Now, SP = CP + Profit

= Rs 750 + Rs 37.50

= Rs 787.50

**(b)** ∵ Total cost price = Rs 1150 + Rs 50 (Overhead expenses)

= Rs 1200

∴ Profit = 5% of Rs 1200

= 5/100 * Rs 1200

= Rs 5 * 12 = Rs 60

Now, SP = CP + Profit

= Rs 1200 + Rs 60

= Rs 1260

**(c)** ∵ Total cost price = Rs 560 + Rs 40 (Overhead expenses)

= Rs 600

∴ Profit = 5% of Rs 600

= 5/100 * Rs 600

= Rs 5 * 6 = Rs 30

Now, SP = CP + Profit

= Rs 600 + Rs 30

= Rs 630

**Question 2.** A shopkeeper bought two TV sets at Rs 10,000 each. He sold one at a profit 10% and the other at a loss of 10%. Find whether he made an overall profit or loss.

**Solution:** Total CP of both TV’s = 2 x Rs 10,000

= Rs 20,000

For 1st TV: CP = Rs 10,000.

Profit rate = 10%

∴ Profit = 10% or Rs 10,000

= 10/100 * Rs 10,000 = Rs 1000

∴ SP = Rs 10,000 + Rs 1000 = Rs 11,000

For 2nd TV: CP = Rs 10,000

Loss rate = 10%

∴ Loss = 10% of Rs 10,000

= 10/100 * Rs 10,000 = Rs 1000

∴ SP = CP – Loss

= Rs 10,000 – Rs 1000 = Rs 9000

Now, Total SP of both the TV’s = Rs 11,000 + Rs 9000

= Rs 20,000

∵ Cost price = Selling price

∴ There is no overall profit or loss.

**Question 1.** Find the buying price of each of the following when 5% ST is added on the purchase of

(a) A towel at Rs 50

(b) Two bars of soap at Rs 35 each

(c) 5 kg of flour at Rs 15 per kg

**Solution:**

**(a)** Cost of the towel = Rs 50

∴ Sales tax on the towel = 5% of Rs 50

= Rs 5/100 * 50 = Rs 2.5

Thus, the buying price of the towel = Rs 50 + Rs 2.5

= Rs 52.5

**(b)** ∵ Cost of the two soap bars = (Rs 35) * 2 = Rs 70

∴ Sales tax = 5% of Rs 70

= Rs 5/100 * 70 = Rs 3.5

Thus, the buying price = Rs 70 + Rs 3.5

= Rs 73.5

**(c) **∵ Cost of 5 kg of flour = Rs 15 * 5 = Rs 75

∴ Sales tax = 5% of Rs 75

= Rs 5/100 * 75

= Rs 375/100 = Rs 3.75

Thus, the buying price = Rs 75 + Rs 3.75

= Rs 78.75

**Question 2.** If 8% VAT is included in the prices, find the original price of

(a) A TV bought for Rs 13,500 (b) A shampoo bottle bought for Rs 180

**Solution:**

**(a)** Cost of TV including VAT = Rs 13500

Rate of VAT = 8%

Let the original price = Rs x

∴ x + 8% of x = Rs 13,500

or x + 8/100 x = Rs 13500

or

or

**or **

Thus, the original price = Rs 12500.

**(b)** Let original price = Rs x

∴ Price including VAT = Rs x + 8% of x

But the original price + VAT = Rs 180

∴

or

Thus, the original price = Rs 166 2/3

**Question 1.** Two times a number is a 100% increase in the number. If we take half the number, what would be the decrease in per cent?

**Solution: **Let the number be x.

∴ Decrease in the number = 1/2 of x

= 1/2 of x = x/2

= 1/2 *100 % = 50%

**Question 2.** By what per cent is Rs 2,000 less than Rs 2,400? Is it the same as the per cent by which Rs 2,400 is more than Rs 2,000?

**Solution: **

Case I

Here 2000 < 2400.

i.e. 2400 is reduced to 2000.

∴ Decrease = 2400 – 2000 = 400

Thus Decrease % =

Thus, Decrease % =

**Case II**

2000 is increased to 2400.

∴ Increase = 2400 – 2000 = 400

∴ Decrease % = 400/2000 x 100% = 20%

Thus, Decrease % = 20%

Obviously, they are not same.

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