1. A shopkeeper calculate percentage profit on the buying price and another on the selling price. What will be their difference in profits if both claim a profit of 20% on goods sold for Rs. 3000?

a) Rs. 200

b) Rs. 100

c) Rs. 150

d) Rs. 400

Explanation: For 20% profit on selling price means $$\frac{1}{5}$$ of 3000 i.e. Rs. 600

Now, let the C.P = Rs. 100, Then,

S.P with 20% profit = Rs. 120

For 20% profit on selling price means cost is 100 + profit is 20 = selling price is 120.

Means selling price is 120% of cost price.

Now selling price is 120% ie 3000 then find 100% amount which will be cost.

Cost = $$\frac{{3000}}{{120}}\% $$

= $$\frac{{3000}}{{\frac{6}{5}}}$$

Because, 120% = $$\frac{6}{5}$$

= 3000 x $$\frac{5}{6}$$

= 2500

Cost is 2500

Thus profit is 20% i.e. $$\frac{1}{5}$$ x 2500 = 500

Difference is 600 - 500 = Rs.100

2. A dishonest dealer marks up the price of his goods by 20% and gives a discount of 10% to the customer. Besides, he also cheats both his supplier and his buyer by 100 grams while buying or selling 1 kilogram. Find the percentage profit earned by the shopkeeper?

a) 20%

b) 25%

c) 32%

d) 50%

Explanation:

**While buying,**

He buys 1100 gram instead of 1000 gram.

Suppose he bought 1100 grams for Rs. 1000.

**While selling,**

He sells only 900 grams when he takes the money for 1 kg.

Now, according to the problem,

he sells at a 8% profit (20% markup, 10% discount).

Hence, his selling price is Rs. 1080 for 900 grams.

1100 grams for Rs. 1000

Hence, 1188 grams for Rs. 1080

Selling: 900 grams for Rs. 1080

Hence, % profit = $$\frac{{288}}{{900}}$$ × 100 = 32%

(using goods left by goods sold formula)

3. A tradesman marks his goods at 25% above the cost price and allows purchasers a discount of $$\frac{{25}}{2}$$%, his profit is:

a) 8%

b) 8.5%

c) 8.625%

d) 9.375%

Explanation:

Let C.P = Rs. 100

Marked Price(M.P) = 100 + 25% of 100 = 125

Now, discount = $$\frac{{25}}{2}$$% on M.P

So, S.P = 125 - $$\frac{{25}}{2}$$% of 125 = Rs. 109.375

%Gain = 9.375%

4. Profit on selling 10 candles equals selling price of 3 bulbs. While loss on selling 10 bulbs equal selling price of 4 candles. Also profit percentage equals to the loss percentage and cost of a candle is half of the cost of a bulb. What is the ratio of selling price of candles to the selling price of a bulb?

a) 5 : 4

b) 3 : 2

c) 4 : 5

d) 3 : 4

Explanation: Candle - - - - - - - - Bulb

CP . . . . A - - - - - - - - B

SP . . . . C - - - - - - - - D

$$\eqalign{ & and.\,C = 2A \cr & {\text{Profit}} = 10\left( {B - A} \right) = 3D \cr & {\text{Loss}} = 10\left( {C - D} \right) = 4B \cr & {\text{Profit}}\% = \frac{{ {3D \times 100} }}{{10A}} \cr & {\text{Loss}}\% = \frac{{ {4B \times 100} }}{{10C}} \cr & \frac{{ {3D \times 100} }}{{10A}} = \frac{{ {4B \times 100} }}{{10C}} \cr & \frac{B}{D} = \frac{3}{2} = 3:2 \cr} $$

5. Find the selling price of goods if two salesmen claim to make 25% profit each, one calculating it on cost price while another on the selling price, the difference in the profits earned being Rs. 100 and selling price being the same in both the cases?

a) Rs. 1200

b) Rs. 1600

c) Rs. 2400

d) Rs. 2500

Explanation: Let C.P's be Rs. 1000 each, their respective S.P will be,

1000 == 25%↑ ⇒ 1250 [person calculating profit on the C.P]

1000 == 33.33%↑ ⇒ 1333.33 [The person calculating his profit on S.P: 25% of S.P = 33.33% of C.P]

The difference turned out to be = 83.33. This has occured when we have assumed the C.P as 1000. But, we are given difference of Rs. 100

So, on comparing,

83.33 = 1000

1 = $$\frac{{1000}}{{83.33}}$$

100 = $$\frac{{1000}}{{83.33}} \times 100$$ = Rs. 1200

6. Cost price of 12 oranges is equal to the selling price of 9 oranges and the discount on 10 oranges is equal to the profit on 5 oranges. What is the percentage point difference between the profit percentage and discount percentage?

a) 20

b) 22.22

c) 16.66

d) 15

Explanation: 12 C.P = 9 S.P,

So profit % = $$\frac{{12\,{\text{C}}{\text{.P}}{\text{.}} - 9\,{\text{C}}{\text{.P}}{\text{.}}}}{{9\,{\text{C}}{\text{.P}}{\text{.}}}}$$ = 33.33.

Then it is said that,

5 S.P - 5 C.P = 10 M.P -10 S.P

From that we get relation between M.P and S.P, that is,

27 S.P = 24 M.P(With help of 12 C.P = 9 S.P)

Then Discount % = $$\frac{{{\text{M.P}} - {\text{S.P}}}}{{{\text{M.P}}}}$$ =

**11.11%**

So, % point discount = 33.33% - 11.11% = 22.22%

7. A retailer increase the selling price by 25% due to which his profit percentage increase from 20% to 25%. What is the percentage increase in cost price ?

a) 20%

b) 30%

c) 25%

d) 50%

Explanation: 100 (Initial C.P) -- 20%↑ (initial profit) → 120(S.P)

120 (S.P) -- 25%↑ → 150 (New S.P)

Let x be the new Cost price

Selling Price = 150

x × 1.25 = 150

x = 120

% change = $$ {\frac{{120 - 100}}{{100}}} \times 100$$ = 20%

8. Two successive price increase of 10% and 10% of an article are equivalent to a single price increase of:

a) $$26\frac{2}{3}$$

b) 25%

c) 21%

d) $$33\frac{1}{3}$$

Explanation: 100 --- 10%↑ → 110 --- 10%↑ → 121

Equivalent price increase = 21%

9. A tradesman fixed his selling price of goods at 30% above the cost price. He sells half the stock at this price, one-quarter of his stock at a discount of 15% on the original selling price and rest at a discount of 30% on the original selling price. Find the gain percentage altogether?

a) 14.875%

b) 15.375%

c) 15.575%

d) 16.375%

Explanation: Let C.P = 100; then marked price = 130;

Now, revenue

$$ = { {\frac{1}{2}} \times 130 + {\frac{1}{4}} \times 0.85 \times 130 + {\frac{1}{4}} \times 0.7 \times 130} $$

$$\eqalign{ & = 65 + 27.65 + 22.5 \cr & = 115.4 \cr & \% {\text{profit}} = \frac{{15.4 \times 100}}{{100}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 15.4\% \cr} $$

10. A bicycle marked at Rs. 2,000, is sold with two successive discount of 20% and 10%.An additional discount of 5% is offered for cash payment. The selling price of the bicycle at cash payment is:

a) Rs. 1,568

b) Rs. 1,368

c) Rs. 1,468

d) Rs. 1,668

Explanation: Marked Price = 2000

S.P after first Discount of 20% = 2000 - 20% of 2000 = 1600

S.P after second Discount of 10% = 1600 - 10% of 1600 = 1440

Now, the final selling price at cash = 1440 - 5% of 1440 = Rs. 1368