Profit And Loss - Study Mode
[#171] The price of an article is first increased by 20% and later on decreased by 25% due to reduction in sales. Find the net percentage change in final price of the article?
Correct Answer
(D) None of these
Explanation
Solution: Let the price of article is Rs. 100 First increase % = 20% After increase, price of article $$eqalign{
& = 100 imes frac{{120}}{{100}} cr
& = { ext{Rs}}{ ext{.120 }} cr} $$ Second decrease % = 25% After decrease, price of article $$eqalign{
& = 120 - frac{{120 imes 25}}{{100}} cr
& = { ext{Rs}}{ ext{. }}90 cr} $$ Net change percent in price $$eqalign{
& = frac{{100 - 90}}{{100}} imes 100 cr
& = frac{{10}}{{100}} imes 100 cr
& = 10\% cr} $$
[#172] 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?
Correct Answer
(B) 22.22
Explanation
Solution: 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% and, Discount = 11.11% Since, CP : SP : MP = 3 : 4 : 4.5 Profit doubles that of discount. So, % point discount = 33.33% - 11.11% = 22.22% point. Detail Explanation: 12 C.P = 9 S.P, So profit % = $$frac{{12,{ ext{C}}{ ext{.P}}{ ext{.}} - 9,{ ext{C}}{ ext{.P}}{ ext{.}}}}{{9,{ ext{C}}{ ext{.P}}{ ext{.}}}}$$ xa0 xa0 = 33.33. Then it is said that, 5 SP - 5 CP = 10 MP -10 SP From that we get relation between MP and SP, that is, 27 SP = 24 MP(With help of 12 CP = 9 SP) THEN DISCOUNT % = $$frac{{{ ext{MP}} - { ext{SP}}}}{{{ ext{MP}}}}$$ xa0 = 11.11% So, % point discount = 33.33% - 11.11% = 22.22%
[#173] 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?
Correct Answer
(B) 3 : 2
Explanation
Solution: Candle - - - - - - - - Bulb CP . . . . A - - - - - - - - B SP . . . . C - - - - - - - - D $$eqalign{
& and.,C = 2A cr
& { ext{Profit}} = 10left( {B - A}
ight) = 3D cr
& { ext{Loss}} = 10left( {C - D}
ight) = 4B cr
& { ext{Profit}}\% = frac{{ {3D imes 100} }}{{10A}} cr
& { ext{Loss}}\% = frac{{ {4B imes 100} }}{{10C}} cr
& { ext{Now,}},{ ext{By}},{ ext{the}},{ ext{questions}}, cr
& frac{{ {3D imes 100} }}{{10A}} = frac{{ {4B imes 100} }}{{10C}} cr
& frac{B}{D} = frac{3}{2} = 3:2 cr} $$
[#174] 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?
Correct Answer
(B) 11.11% loss
Explanation
Solution: $$eqalign{
& { ext{CP of one egg in }}{{ ext{1}}^{st}}{ ext{ case}} cr
& = frac{1}{3} = 33.33,{ ext{paise}} cr
& { ext{CP of one egg in}},{2^{nd}}{ ext{ case}} cr
& = frac{1}{6} = 16.66,{ ext{paise}} cr
& { ext{Average}},{ ext{CP}} cr
& = frac{{ {33.33 + 16.66} }}{2} cr
& = 25,{ ext{paise}} cr
& { ext{Selling}},{ ext{price}},{ ext{of}},{ ext{9}},{ ext{eggs}} cr
& = Rs.,2 cr
& { ext{SP}},{ ext{of}},{ ext{one}},{ ext{egg}} cr
& = frac{{200}}{9} cr
& { ext{Profit}},{ ext{or}},{ ext{loss}} cr
& = frac{{ {left( {25 - {frac{{200}}{9}} }
ight) imes 100} }}{{25}} cr
& { ext{Profit}},{ ext{or}},{ ext{loss}} cr
& = 11.11,({ ext{loss}}) cr} $$
[#175] 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?
Correct Answer
(A) Rs. 1200
Explanation
Solution: 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 So, on comparing, 83.33 = 1000 1 = $$frac{{1000}}{{83.33}}$$ 100 = $$frac{{1000}}{{83.33}} imes 100$$ xa0 = Rs. 1200