Examples on Profit and Loss are as follows.



1. A dealer gains $ 200 when he sells on article at a profit of 10 %. Find the selling price (S.P.) of the article.

Solution:

Let the cost price (C.P.) be $ 100.

Therefore selling price (S.P.) = cost price (C.P.) + Profit

= $ 100 + $ 10

= $ 110.

If the gain is $ 10, then the S.P. is $ 110.

If the gain is $ 1, then the S.P. is $ ¹¹⁰/₁₀.

If the gain is $ 200, then the S.P. is $ (¹¹⁰/₁₀ × 200)

= $ ^{(110 × 200)}/₁₀

= $ 2,200.

Hence, the selling price (S.P.) of the article is $ 2,200.



2. A man sold two tape recorders at $ 3,000 each. On one he gains 20 % and on the other he loses 20 %. What percent does he gain on the whole transaction?

Solution:

For the first tape recorder:

Gain = 20 %.

Let cost price (C.P.) = $ 100.

Therefore, selling price (S.P.) = $ (100 + 20)

= $ 120.

When selling price (S.P.) is $ 120, cost price (C.P.) is $ 100.

Therefore, when selling price (S.P.) is $ 300, cost price (C.P.)

= $ ¹⁰⁰/₁₂₀ × 300

= $ ^{(100 × 300)}/₁₂₀

= $ ³⁰⁰⁰⁰/₁₂₀

= $ 2,500.

Therefore, cost price (C.P.) of the first tape recorder = $ 2,500.

For the second tape recorder:

Loss = 20 %.

Let cost price (C.P.) = $ 100.

Therefore, selling price (S.P.) = $ (100-20)

= $ 80.

When selling price (S.P.) is $ 80,

the cost price (C.P.) is $ 100.

Therefore, when selling price (S.P.) is $ 300, the cost price (C.P.)

= $ ¹⁰⁰/₈₀ x 300

= $ ^{(100 x 300)}/₈₀

= $ ³⁰⁰⁰⁰/₈₀

= $ 3,750.

Therefore, cost price (C.P.) of the second tape recorder = $ 3,750.

Thus, total cost price (C.P.) of two tape recorders = $ 2,500 + $ 3,750

= $6,250.

Total selling price (S.P.) of two tape recorders = $ (2 x 3,000)

= $ 6,000.

Thus, cost price (C.P.) > selling price (S.P.) so, there is a loss

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

= $ 6,250 - $ 6,000

= $ 250.

Percentage loss = ^Loss/_{Cost price (C.P.)} × 100

= ²⁵⁰/₆₂₅₀ × 100

= ^{(250 × 100)}/₆₂₅₀

= ²⁵⁰⁰⁰/₆₂₅₀

= 4 %.

Hence, the man loses 4 % on the whole transaction.



3. A person bought 50 dozen eggs at $ 8 a dozen. Out of these, 20 eggs were found broken. He sold the remaining eggs at $ 0.80 per egg. Find his gain or loss percent.

Solution:

Cost price (C.P.) of 50 dozen eggs = $ 8 x 50 = $ 400.

Number of broken eggs = 20.

Total number of eggs = 50 x 12 = 600.

Number of good eggs = 600 - 20 = 580.

Selling price (S.P.) of 580 eggs = $ 0.80 x 580 = $ 464.

Since, selling price (S.P.) > cost price (C.P.), there is a profit.

Profit = selling price (S.P.) - cost price (C.P.)

= $ (464 - 400)

= $ 64.

Profit % = ^Profit/_{Cost Price (C.P.)} × 100

= ⁶⁴/₄₀₀ × 100

= ^{(64 × 100)}/₄₀₀

= ⁶⁴⁰⁰/₄₀₀

= 16.

Hence, profit = 16 %.



4. A dealer bought 18 tables at $ 550 per table. He sold 12 of them at $ 650 per table and the remaining tables at $ 500 per table. Find his gain or loss percent.

Solution:

Cost price (C.P.) of 18 tables = $ 550 x 18 = $ 9,900.

Selling price (S.P.) of 12 tables = $ 650 x 12 = $ 7,800.

Number of remaining tables = 18 - 12 = 6.

Selling price (S.P.) of remaining 6 tables = $ 500 x 6 = $ 3,000.

Total selling price (S.P.) of 18 tables = $ 7,800 + $ 3,000 = $ 10,800.

Since, selling price (S.P.) > cost price (C.P.), there is a profit.

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

= $ 10,800 - 9,900

= $ 900.

Profit % = ^Profit / _{Cost price (C.P.)} × 100

= ⁹⁰⁰/₉₉₀₀× 100

= ^{(900 × 100)}/₉₉₀₀

= ⁹⁰⁰⁰⁰/₉₉₀₀

= ¹⁰⁰/₁₁

=9¹/₁₁.

Hence, profit = 9¹/₁₁ %.



5. If the selling price of 20 pens is the same as the cost price of 21 pens. Find the profit percent.

Solution:

Let cost price of each pen be $ 1.

Cost price (C.P.) of 20 pens = $ 1 x 20 = $ 20.

Selling price (S.P.) of 20 pens = Cost price (C.P.) of 21 pens = $ 21.

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

= $ 21 - $ 20 = $ 1.

Profits % = ^Profit / _{Cost price (C.P.)} × 100

= ¹/₂₀ × 100

= ^{(1 × 100)}/₂₀

= ²⁰⁰/₂₀

= 5 %.

Hence, profit = 5 %.



6. A rice merchant sold 600 quintals of rice at a profit of 7 %. If a quintal of rice cost him $ 250 and his total overhead charges for transportation, etc., were $ 1,000, find his total profit and the selling price of 600 quintals of rice.

Solution:

Cost of one quintal of rice – $ 250.

Therefore, cost of 600 quintals of rice = $ (250 x 600) = $ 150,000.

Overhead charges = $ 1,000.

Hence, Cost price (C.P.) = $ (150,000 + 1,000) = $ 151,000.

Profit = 7 %.

Net Profit = 7 % of $ 151,000

= $ ⁷/₁₀₀ x 151,000

= $ ^{(7 x 151,000 )}/₁₀₀

= $ ^1057000/₁₀₀

= $ 10,570.

Selling price (S.P.) = Cost price (C.P.) + Profit

= $ (151,000 + 10,570) = $ 161,570.

Thus, total profit is $ 10,570 and the selling price is $ 161,570.