Profit And Loss - Study Mode

[#216] Raju purchased an item for Rs. 8200 and sold it at a gain of 25% . From that amount he purchased another item and sold it at a loss of 20% . What is his overall gain loss ?
Correct Answer

(D) Neither loss nor gain

Explanation

Solution: $$eqalign{
& { ext{Initial investment}} cr
& = { ext{Rs}}.8200 cr
& { ext{S}}{ ext{.P}}{ ext{.of }}{{ ext{1}}^{{ ext{st}}}}{ ext{ term}} cr
& = { ext{Rs}}.left( {frac{{125}}{{100}} imes 8200}
ight) cr
& = { ext{Rs}}{ ext{. }}10250 cr
& { ext{C}}{ ext{.P}}{ ext{.of }}{{ ext{2}}^{{ ext{nd}}}}{ ext{ term}} cr
& = { ext{Rs}}{ ext{. }}10250 cr
& { ext{loss}} = 20\% cr
& { ext{Final receipt}} cr
& = { ext{S}}{ ext{.P}}{ ext{.of }}{{ ext{2}}^{{ ext{nd}}}}{ ext{ term}} cr
& = { ext{Rs}}.left( {frac{{80}}{{100}} imes 10250}
ight) cr
& = { ext{Rs}}{ ext{. }}8200 cr} $$ Since initial investment = final receipt, there was neither gain nor loss.

[#217] If the selling price of an article is doubled, then its loss profit percent is converted into equal profit percent. The loss percent on the article is = ?
Correct Answer

(C) $$33frac{1}{3}$$ %

Explanation

Solution: Let SP = Rs. x According to question, $$eqalign{
& left( {frac{{CP - x}}{{CP}}}
ight) imes 100 = left( {frac{{2x - CP}}{{CP}}}
ight) imes 100 cr
& CP - x = 2x - CP cr
& 3x = 2CP cr
& x = frac{2}{3}CP cr
& SP = frac{2}{3}CP cr
& frac{{SP}}{{CP}} = frac{2}{3} > 1{ ext{ unit loss}} cr
& { ext{Loss}}\% = frac{1}{3} imes 100 = 33frac{1}{3}\% cr} $$

[#218] If an article sold at 200% profit then the ratio of its cost price to his selling price will be = ?
Correct Answer

(C) 1 : 3

Explanation

Solution: Let the cost price of the article is = Rs. 100 According to the question, [{ ext{100 (cp)}}xrightarrow{{200\% { ext{ profit}}}}{ ext{300 (sp)}}] [{ ext{Ratio of }}frac{{{ ext{CP}}}}{{{ ext{SP}}}} = frac{{100}}{{300}} = frac{1}{3}]

[#219] A fruit seller makes a profit of 20% by selling mangoes at a certain price. If he charges Rs. 1 more for each mango, he can make a profit of 40% . Find the selling price of a mango in the first case = ?
Correct Answer

(A) Rs. 6

Explanation

Solution: Let CP of 1 mango → 100 CP SP 100 → 120 [Profit→20] 100 → 140 [Profit→40] Difference in SP = 140 - 120 = 20 20 unit = Rs. 1 1 unit = $$frac{1}{{20}}$$ 120 unit = $$frac{120}{{20}}$$ = Rs. 6

[#220] If selling price of an article is $$frac{4}{3}$$ of its cost price, the profit in the transaction is -
Correct Answer

(D) $$33frac{1}{3}$$ %

Explanation

Solution: $$eqalign{
& { ext{Let C}}{ ext{.P}}{ ext{.}} = { ext{Rs}}{ ext{. }}x. cr
& Then,S.P. = { ext{Rs}}.frac{{4x}}{3} cr
& Gain = { ext{Rs}}.left( {frac{{4x}}{3} - x}
ight) cr
& ,,,,,,,,,,,,, = { ext{Rs}}{ ext{. }}frac{x}{3} cr
& herefore { ext{Gain }}\% cr
& = left( {frac{x}{3} imes frac{1}{x} imes 100}
ight)\% cr
& = 33frac{1}{3}\% cr} $$