True Discount - Study Mode

[#81] A shopkeeper marks his goods 20% above his cost price and gives 15% discount on the marked price. His gain percent is = ?
Correct Answer

(C) 2%

Explanation

Solution: Let the cost price = Rs. 100 $$eqalign{
& { ext{Market price }} cr
& { ext{ = 120}}\% { ext{ of 100 }} cr
& { ext{ = Rs}}{ ext{. 120}} cr
& { ext{Selling price }} cr
& { ext{ = 85}}\% { ext{ of 120 }} cr
& { ext{ = }}frac{{85}}{{100}} imes { ext{120 }} cr
& { ext{ = Rs}}{ ext{. 102}} cr
& { ext{Gain }}\% = frac{{102 - 100}}{{100}} imes 100 cr
& ,,,,,,,,,,,,,,,,,,,, = 2\% cr} $$

[#82] A shopkeeper sold an item for Rs. 1510 after giving a discount of $$24frac{1}{2}\% $$ xa0 and there by incurred a loss of 10%. Had he sold the item without discount his net profit would have been = ?
Correct Answer

(D) $${ ext{Rs}}{ ext{. 322}}frac{2}{9}$$

Explanation

Solution: Let the marked price of an item = Rs. x Selling price of an item $$ = left( {100 - 24frac{1}{2}}
ight)\% ,{ ext{of }}x$$ $$eqalign{
& Rightarrow 1510 = frac{{151}}{2} imes frac{1}{{100}} imes x cr
& Rightarrow x = { ext{Rs}}{ ext{. 2000}} cr
& { ext{Cost price of an item }} cr
& = 1510 imes frac{{100}}{{90}} cr
& { ext{ = Rs}}{ ext{. }}frac{{15100}}{9} cr
& { ext{Without discount, gain}} cr
& { ext{ = }}2000 - frac{{15100}}{9} cr
& = frac{{18000 - 15100}}{9} cr
& = frac{{2900}}{9} cr
& = { ext{Rs}}{ ext{. 322}}frac{2}{9} cr} $$

[#83] Discount on a pair of shoes marked at Rs. 475 and discounted at 15% is = ?
Correct Answer

(C) Rs. 71.25

Explanation

Solution: Market price of shoes = Rs. 475 $$eqalign{
& { ext{Discount}} = frac{{15}}{{100}} imes 475 cr
& ,,,,,,,,,,,,,,,,,,,,,,,,, = frac{{285}}{4}{ ext{ }} cr
& ,,,,,,,,,,,,,,,,,,,,,,,{ ext{ = Rs 71}}{ ext{.25}} cr} $$

[#84] A machine is marked at Rs. 6800 and available at a discount of 10%. The shopkeeper gives another off season discount to the buyer and sells the machine for Rs. 5202. Find the off season discount ?
Correct Answer

(C) 15%

Explanation

Solution: Marked price of machine = Rs. 6800 After 1st discount $$eqalign{
& = frac{{90}}{{100}} imes 6800 cr
& = { ext{Rs}}{ ext{. 6120}} cr} $$ Selling price of machine = Rs. 5202 $$eqalign{
& { ext{Discount }}\% cr
& = frac{{6120 - 5202}}{{6120}} imes 100 cr
& = frac{{918}}{{6120}} imes 100 cr
& = 15\% cr} $$

[#85] A double bed is market at Rs. 75000. The shopkeeper allows successive discounts of 8%, 5% and 2% on it. What is the net selling price ?
Correct Answer

(C) Rs. 64239

Explanation

Solution: $$eqalign{
& { ext{Net selling price }} cr
& { ext{ = }}frac{{92}}{{100}} imes frac{{95}}{{100}} imes frac{{98}}{{100}} imes 75000 cr
& = { ext{Rs}}{ ext{. 64239}} cr} $$