Profit And Loss - Study Mode

[#236] A discount series of p% and q% on an invoice is the same as a single discount of -
Correct Answer

(D) None of these

Explanation

Solution: Let marked price be Rs. 100 Then, S.P. = (100 - q)% of (100 - p)% of Rs. 100 $$eqalign{
& = { ext{Rs}}{ ext{.}}left[ {frac{{100 - { ext{q}}}}{{100}} imes frac{{100 - { ext{p}}}}{{100}} imes 100}
ight] cr
& = { ext{Rs}}.left[ {frac{{left( {100 - { ext{q}}}
ight)left( {100 - { ext{p}}}
ight)}}{{100}}}
ight] cr
& herefore { ext{Single discount }} cr
& = left{ {100 - left[ {frac{{left( {100 - { ext{q}}}
ight)left( {100 - { ext{p}}}
ight)}}{{100}}}
ight]}
ight}\% cr
& = left( {{ ext{p}} + { ext{q}} - frac{{{ ext{pq}}}}{{100}}}
ight)\% cr} $$

[#237] If the cost price is 90% of the selling price, what is the profit percent ?
Correct Answer

(D) $$11frac{1}{9}$$%

Explanation

Solution: According to the question, $$eqalign{
& { ext{C}}{ ext{.P}}{ ext{. = }}frac{{90}}{{100}}{ ext{S}}{ ext{.P}}{ ext{.}} cr
& frac{{{ ext{C}}{ ext{.P}}{ ext{.}}}}{{{ ext{S}}{ ext{.P}}{ ext{.}}}}{ ext{ = }}left. {frac{9}{{10}}}
ight
angle { ext{1 unit profit}} cr
& { ext{Profit }}\% = frac{1}{9} imes 100 cr
& ,,,,,,,,,,,,,,,,,,,,,, = 11frac{1}{9}\% { ext{ }} cr} $$

[#238] An item when sold for Rs. 1690 earned 30% profit on the cost price. Then the cost price is = ?
Correct Answer

(C) Rs. 1300

Explanation

Solution: Let the cost price is x According to question $$eqalign{
& Rightarrow x imes frac{{100 + 30}}{{100}} = 1690 cr
& Rightarrow x imes frac{{130}}{{100}} = 1690 cr
& herefore x = frac{{1690 imes 100}}{{130}} cr
& ,,,,,,,,,, = { ext{Rs}}{ ext{.}},1300 cr} $$

[#239] A bought an article, paying 5% less than the original price. A sold it with 20% profit on the price he had paid. What percent of profit did A earn on the original price = ?
Correct Answer

(C) 14

Explanation

Solution: $$eqalign{
& { ext{Real}},{ ext{Price}} = 100 cr
& { ext{CP}} = 95 cr
& { ext{SP}} = 95 imes frac{{120}}{{100}} cr
& ,,,,,,,,, = 114 cr
& herefore { ext{Profit}}\% = 14\% cr} $$

[#240] A shop gives 10% discount on the purchase of an item. If paid for in cash immediately, a further discount of 12% is given. If the original price of the item is Rs. 250, what is the price of the article if a cash purchase is made ?
Correct Answer

(C) Rs. 198

Explanation

Solution: S.P. = 88% of 90% of Rs. 250 $$eqalign{
& = { ext{Rs}}.left( {frac{{88}}{{100}} imes frac{{90}}{{100}} imes 250}
ight) cr
& = { ext{Rs}}.198 cr} $$