Profit And Loss - Study Mode

[#56] A fruit seller professes to sell his fruits at cost price, but still gains 25% on his outlay. What weight does he substitute for a kilogram ?
Correct Answer

(A) 800 gm

Explanation

Solution: $$eqalign{
& { ext{Let error}} = x{ ext{ gms}}{ ext{.}} cr
& { ext{Then,}} cr
& = frac{x}{{1000 - x}} imes 100 = 25 cr
& Leftrightarrow frac{{100x}}{{1000 - x}} = 25 cr
& Leftrightarrow 100x = 25000 - 25x cr
& Leftrightarrow 125x = 25000 cr
& Leftrightarrow x = 200 cr
& herefore { ext{Weight used}} cr
& = (1000 - 200){ ext{gms}} cr
& = { ext{800 gms}}. cr} $$

[#57] A shopkeeper cheats to the extent of 10% while buying as well as selling, by using false weights. His total gain is -
Correct Answer

(D) 21%

Explanation

Solution: $$eqalign{
& { ext{Rule}}:{ ext{Gain}}\% cr
& = frac{{{{left( {100 + { ext{common gain}}\% }
ight)}^2}}}{{100}} - 100 cr
& herefore { ext{Gain }}\% cr
& = left[ {frac{{{{left( {100 + 10}
ight)}^2}}}{{100}} - 100}
ight]\% cr
& = left( {frac{{12100 - 10000}}{{100}}}
ight)\% cr
& = 21\% cr} $$

[#58] How much percent above the cost price should a shopkeeper marks his goods so as to earn a profit of 32% after allowing a discount of 12% on the marked price = ?
Correct Answer

(A) 50%

Explanation

Solution: According to the question, Cost Price : Marked Price (100 - Discount%) : (100 + Profit%) 100 - 12 : 100 + 32 88 : 132 44 units hike $$eqalign{
& herefore { ext{Hike}}\% = frac{{44}}{{88}} imes 100 cr
& ,,,,,,,,,,,,,,,,,,,,,, = 50\% cr} $$

[#59] A dealer purchased a washing machine for Rs. 7660. After allowing a discount of 12% on its marked price, he still gains 10% . Find the marked price of the washing machine = ?
Correct Answer

(A) Rs. 9575

Explanation

Solution: According to the question, Cost Price : Marked Price (100 - Discount) : (100 + Profit) 100 - 12 : 100 + 10 88 : 110 $$mathop {frac{{1915}}{{22}} imes downarrow }limits_{{ ext{Rs}}{ ext{.7660(Cost Price)}}} :mathop { downarrow imes frac{{1915}}{{22}}}limits_{x08oxed{{ ext{Rs}}{ ext{.9575(MP)}}}} $$

[#60] A publisher printed 2000 copies of a book at a cost of Rs. 70000. He distributes 400 copies free as specimen copies. He gave 30% discount on marked price of each book which is Rs. 75. What is his gain or loss percentage = ?
Correct Answer

(A) 20% gain

Explanation

Solution: According to the question, Cost price of 2000 books are = Rs. 70000 Cost price of 1 book is $$ = frac{{70000}}{{2000}} = { ext{Rs}}{ ext{. 35}}$$ Marked price of 1 book is = Rs. 75 Discount = 30% Selling price of 1 book = Rs. 52.5 He distribute 400 books free Selling price of 1600 books = 52.5 × 1600 = Rs. 84000 Profit = Selling price - Cost price = 84000 - 70000 = Rs. 14000 $$eqalign{
& { ext{Profit }}\% = frac{{14000}}{{70000}} imes 100 cr
& ,,,,,,,,,,,,,,,,,,,,, = 20\% { ext{ gain}} cr} $$