1. 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: Ratio of selling price and Cost Price,

SP : CP = 12 : 9 =4 : 3

Profit of 3 oranges = Rs. 1 (Let CP = Rs. 1)

Profit = $$\frac{1}{3}$$ = 33.33%

Discount = 11.11%

CP : SP : MP = 3 : 4 : 4.5

Profit doubles that of discount.

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

2. 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

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

3. An egg seller sells his eggs only in the packs of 3 eggs, 6 eggs, 9 eggs, 12 eggs etc., but the rate is not necessarily uniform. One day Raju (which is not the same egg seller) purchased at the rate of 3 eggs for a rupee and the next hour he purchased equal number of eggs at the rate of 6 eggs for a rupee. Next day he sold all the eggs at the rate of 9 eggs for Rs. 2. What is his percentage profit or loss?

a) 10% loss

b) 11.11% loss

c) 3% loss

d) 2.5% profit

Explanation:

$$\eqalign{ & {\text{CP of one egg in }}{{\text{1}}^{st}}{\text{ case}} \cr & = \frac{1}{3} = 33.33\,{\text{paise}} \cr & {\text{CP of one egg in}}\,{2^{nd}}{\text{ case}} \cr & = \frac{1}{6} = 16.66\,{\text{paise}} \cr & {\text{Average}}\,{\text{CP}} \cr & = \frac{{ {33.33 + 16.66} }}{2} \cr & = 25\,{\text{paise}} \cr & {\text{Selling}}\,{\text{price}}\,{\text{of}}\,{\text{9}}\,{\text{eggs}} \cr & = Rs.\,2 \cr & {\text{SP}}\,{\text{of}}\,{\text{one}}\,{\text{egg}} \cr & = \frac{{200}}{9} \cr & {\text{Profit}}\,{\text{or}}\,{\text{loss}} \cr & = \frac{{ {\left( {25 - {\frac{{200}}{9}} } \right) \times 100} }}{{25}} \cr & {\text{Profit}}\,{\text{or}}\,{\text{loss}} \cr & = 11.11\,{\text{loss}} \cr} $$

4. 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 CP's be Rs. 1000 each, their respective SP will be,

1000 == 25%↑ ⇒ 1250 [person calculating profit on the CP]

1000 == 33.33%↑ ⇒ 1333.33 [The person calculating his profit on SP: 25% of SP = 33.33% of CP]

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

On comparing,

83.33 = 1000

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

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

5. 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

let CP = Rs. 100,

SP 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

6. A pharmaceutical company made 3000 strips of tablets at a cost of Rs. 4800. The company gave away 1000 strips of tablets to doctors as free samples. A discount of 25% was allowed on the printed price. Find the ratio profit if the price is raised from Rs. 3.25 to Rs. 4.25 per strip and if at the latter price, samples to doctors were done away with. (New profit / Old profit).

a) 55.5

b) 63.5

c) 75

d) 99.25

Explanation: Total sales revenue (Old) = 2000 × 3.25 × 0.75 = 4875 [0.75 as 25% discount was allowed]

Profit

_{old}= Total sales revenue - 4800

= 4875 - 4800 = 75

Total sales revenue (New) = 3000 × 4.25 × 0.75 = 9562.5 [New price is calculated on doctors samples as well.]

Profit

_{new}= 9562.5 - 4800 = 4762.5

Ratio,

$$\frac{{{\text{Profi}}{{\text{t}}_{{\text{new}}}}}}{{{\text{Profi}}{{\text{t}}_{{\text{old}}}}}} = \frac{{4762.5}}{{75}} = 63.5$$

7. An article costing Rs. 20 was marked 25% above the cost price. After two successive discounts of the same percentage, the customer now pays Rs. 20.25. What would be the percentage change in profit had the price been increased by the same percentage twice successively instead reducing it?

a) 3600%

b) 3200%

c) 2800%

d) 4000%

Explanation: The successive discounts must have been of 10% each As

20 (CP) == 25%↑ ⇒ 25(MP) == 10↓ ⇒ 22.5 == 10%↓ ⇒ 20.25(SP)

Profit = 20.25 - 20 = 0.25

Increased percentage if price have been increased twice successively instead of reducing it,

20(MP) == 10%↑ ⇒ 27.5 == 10%↑ ⇒ 30.25

Profit = 30.25 - 20 = 10.25.

Profit Change = 10.25 - 0.25 = 10

Percentage Profit change,

= $$\frac{{10 \times 100}}{{0.25}}$$

= 4000%

8. A pen company produces very fine quality of writing pens. Company knows that on average 10% of the produced pens are always defective so are rejected before packing. Company promises to deliver 7200 pens to its wholesaler at Rs. 10 each. It estimates the overall profit on all the manufactured pens to be 25%. What is the manufactured cost of each pen?

a) Rs. 6

b) Rs. 7.2

c) Rs. 5.6

d) Rs. 8

Explanation: The company is able to deliver 90% of the manufactured pens. Means to produce 7200 pens they must have to produce 8000 pens as 10% are defectives.

So, let K be the manufacturing price of each pen.

Total income (including 25% profit) = 8000 × K × 1.25

This same income is obtained by selling 90% manufactured pens at Rs. 10 which is equal to 7200 × 10

8000 × K × 1.25 = 7200 × 10

K = Rs. 7.2 [90% of 8000 = 7200]

9. A company charges a fixed rental of Rs. 350 per month. It allows 200 calls free per month. Each call is charge at Rs. 1.4 when the number of calls exceed 200 per month and it charges Rs. 1.6 when the number of calls exceeds 400 per month and so on. A customer made 150 calls in February and 250 calls in march. By how much percent each call is cheaper in March than each call in February.

a) 28%

b) 25%

c) 18.5%

d) 16%

Explanation:

$$\eqalign{ & {\text{Charge per call in February}} \cr & = \frac{{350}}{{150}} = \frac{7}{3} = 2.33 \cr & {\text{Charge per call in March}} \cr & = \frac{{ {350 + \left( {50 \times 1.4} \right)} }}{{250}} \cr & = \frac{{420}}{{250}} = \frac{{42}}{{25}} = 1.68 \cr & \% {\text{ Cheaper call rate in March}}. \cr & = {\frac{{ {2.33 - 1.68} }}{{2.33}}} \times 100 \cr & = 28\% \cr} $$

10. In the Bargaining Bazar everyone purchase with a fair bargaining, so the traders markup the prices too much. A trader marked up an article at Rs. M expected huge profit if it is sold on marked price. But a customer purchased it at $$\frac{{\text{M}}}{2}$$ with his fine bargaining skills, so the expected profit of the trader diminished by 66.66%. What is the percentage discount fetched by the customer through bargaining?

a) 33.33%

b) 50%

c) 60%

d) 66.66%

Explanation:

$$\eqalign{ & {\text{MP}} = M \cr & {\text{SP}} = \frac{M}{2} \cr & \% \,{\text{Discount}} \cr & = {\frac{{ {\frac{M}{2}} }}{M}} \times 100 \cr & = 50\% \cr} $$