Profit And Loss - Study Mode

[#116] A dealer sold an article at 6% loss. Had he sold it for Rs. 64 more, he would have made a profit of 10%. Then the cost of the article is = ?
Correct Answer

(A) Rs. 400

Explanation

Solution: Let the cost price of the article = Rs. 100x Loss% = 6% $$eqalign{
& { ext{SP}} = 100x imes frac{{94}}{{100}} = { ext{Rs}}{ ext{.}},94x cr
& { ext{If}},{ ext{SP}},{ ext{is}},{ ext{Rs}}{ ext{.}},{ ext{64}},{ ext{more,}} cr
& Rightarrow { ext{New}},{ ext{SP}} = { ext{Rs}}{ ext{.}},left( {94x + 64}
ight) cr
& Rightarrow { ext{Profit}}\% cr
& frac{{left( {94x + 64}
ight) - 100x}}{{100x}} imes 100 = 10 cr
& Rightarrow 64 - 6x = 10x cr
& Rightarrow 10x + 6x = 64 cr
& Rightarrow 16x = 64 cr
& Rightarrow x = frac{{64}}{{16}} cr
& herefore x = 4 cr
& herefore { ext{Cost}},{ ext{Price}} = 100 imes 4 cr
& ,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,, = { ext{Rs}}{ ext{.}},400 cr} $$

[#117] After successive discounts of 12% and 5% an article was sold for Rs. 209. What was the original price of the article?
Correct Answer

(B) Rs. 250

Explanation

Solution: Let the original price be Rs. x. Then, 95% of 88% of x = 209 $$eqalign{
& Rightarrow x = left( {frac{{209 imes 100 imes 100}}{{95 imes 88}}}
ight) cr
& ,,,,,,,,,,,,, = 250 cr
& ,,,,,,,,,,,,, = { ext{Rs}}{ ext{. }}250 cr} $$

[#118] Two stories A and B mark the price of an item identically. A allows 3 successive discounts of 10% each. B allows 10% discount on the list price and a subsequent discount of 19%. Under the circumstances, which of the following is true?
Correct Answer

(C) The price of the article is same at A and B

Explanation

Solution: Let the M.P. of the item at each of the stories A and B be Rs. 100. Final price at A = 90% of 90% of 90% of Rs. 100 $$eqalign{
& = { ext{Rs}}.left( {frac{{90}}{{100}} imes frac{{90}}{{100}} imes frac{{90}}{{100}} imes 100}
ight) cr
& = { ext{Rs}}{ ext{. }}72.90 cr} $$ Final price at B = 81% of 90% of Rs. 100 $$eqalign{
& = { ext{Rs}}.left( {frac{{81}}{{100}} imes frac{{90}}{{100}} imes 100}
ight) cr
& = { ext{Rs}}{ ext{. }}72.90 cr} $$ Hence, the price of the article is same at A and B

[#119] By selling 4 articles for 1 rupee, a man losses 4%. Had he sold three articles per rupee, the profit would have been = ?
Correct Answer

(B) 28%

Explanation

Solution: Selling price of 4 article = Rs. 1 Loss = 4% Cost price of 4 articles $${ ext{ = 1}} imes frac{{100}}{{96}} = frac{{100}}{{96}}$$ Cost price of 3 articles $${ ext{ = }}frac{{100}}{{96}} imes frac{3}{4} = frac{{75}}{{96}}$$ New selling price of 3 articles = Rs. 1 $$eqalign{
& { ext{Profit }}\% cr
& = frac{{frac{{1 - 75}}{{96}}}}{{frac{{75}}{{96}}}} imes 100 cr
& = frac{{21}}{{75}} imes 100 cr
& = 28\% cr} $$

[#120] By selling 80 ball pens for Rs. 140 a retailer losses 30%. How many ball pens should he sell for Rs. 104 so as to make a profit of 30% ?
Correct Answer

(A) 32

Explanation

Solution: $$eqalign{
& 100x imes frac{{100 - 30}}{{100}} = 140 cr
& Rightarrow 70x = 140 cr
& Rightarrow x = 2 cr
& herefore { ext{CP}} = 100x cr
& ,,,,,,,,,,,,,,, = 100 imes 2 cr
& ,,,,,,,,,,,,,,, = { ext{Rs}}{ ext{.}},200 cr
& { ext{SP}} = 200 imes frac{{left( {100 + 30}
ight)}}{{100}} cr
& ,,,,,,,,, = 260 cr
& { ext{Now,}} cr
& { ext{Rs}}{ ext{.}},260 = 80,{ ext{ball}},{ ext{pens}} cr
& herefore { ext{Rs}}{ ext{.}},104 = frac{{80}}{{260}} imes 104 cr
& ,,,,,,,,,,,,,,,,,,,,,,,,, = 32,{ ext{ball}},{ ext{pens}} cr} $$