True Discount - Study Mode
[#71] For a certain article. If discount is 25% the profit is 25%. If the discount is 10%, then the profit is = ?
Correct Answer
(A) 50%
Explanation
Solution: $$eqalign{
& { ext{For same article}}, cr
& frac{{100 - {d_1}}}{{100 - {d_2}}} = frac{{100 + {g_1}}}{{100 + {g_2}}} cr
& Rightarrow frac{{100 - 25}}{{100 - 10}} = frac{{100 + 25}}{{100 + {g_2}}} cr
& Rightarrow frac{{75}}{{90}} = frac{{125}}{{100 + {g_2}}} cr
& Rightarrow 100 + {g_2} = frac{{90 imes 125}}{{75}} cr
& Rightarrow 100 + {g_2} = 150 cr
& herefore {g_2} = 50\% cr} $$
[#72] A single discount of 50% on an article costing Rs. 10000 is better than two successive discounts of 40% and 10% by = ?
Correct Answer
(A) Rs. 400
Explanation
Solution: $$eqalign{
& { ext{Single discount = 50}}\% cr
& { ext{Two successive discount}} cr
& { ext{ = 40}} + { ext{10}} - frac{{40 imes 10}}{{100}} cr
& = 50 - 4 cr
& = 46 cr
& { ext{Difference}} cr
& = 50 - 46 cr
& = 4\% cr
& { ext{Difference amount }} cr
& { ext{ = 4}}\% { ext{ of 10000}} cr
& { ext{ = }}frac{4}{{100}} imes 10000 cr
& { ext{ = Rs}}{ ext{. 400}} cr} $$
[#73] A purchased a dining table marked at Rs. 3000 at a successive discounts of 10% and 15% respectively. He gave Rs. 105 as trans-portion charge and sold it at Rs. 3200. What is his gain percentage ?
Correct Answer
(C) $$33frac{1}{3}\% $$
Explanation
Solution: Market price of dining table = Rs. 3000 After discount, cost price $$eqalign{
& { ext{ = 3000}} imes frac{{90}}{{100}} imes frac{{85}}{{100}} cr
& { ext{ = Rs}}{ ext{. 2295}} cr} $$ After transport charges = 2295 + 105 $$eqalign{
& { ext{Cost price = Rs}}{ ext{. 2400}} cr
& { ext{Selling price = Rs}}{ ext{. 3200}} cr
& { ext{Profit }}\% { ext{ }} cr
& = frac{{3200 - 2400}}{{2400}} imes 100 cr
& = frac{{800 imes 100}}{{2400}} cr
& = 33frac{1}{3}\% cr} $$
[#74] A shopkeeper marks the price of an article at Rs. 80. What will be the selling price, if he allows two successive discounts at 5% each = ?
Correct Answer
(A) Rs. 72.20
Explanation
Solution: Marked price of article = Rs. 80 $$eqalign{
& { ext{Two successive discount }} cr
& { ext{ = 5}} + 5 - frac{{5 imes 5}}{{100}} cr
& = 10 - 0.25 cr
& = 9.75\% cr
& { ext{Discount of article }} cr
& { ext{ = 9}}{ ext{.75% of 80}} cr
& { ext{ = }}frac{{9.75}}{{100}} imes 80 cr
& = { ext{Rs}}{ ext{. 7}}{ ext{.80}} cr
& { ext{Selling price of article }} cr
& { ext{ = }}80 - 7.80 cr
& { ext{ = Rs}}{ ext{. 72}}{ ext{.20}} cr} $$
[#75] A shopkeeper purchased a chair marked at Rs. 600 at two successive discounts of 15% and 20% respectively, he spent Rs. 28 on transportation and sold the chair for Rs. 545. His gain percent was = ?
Correct Answer
(A) 25%
Explanation
Solution: Marked price of chair = Rs. 600 After discount, cost price $$eqalign{
& { ext{ = 600}} imes frac{{85}}{{100}} imes frac{{80}}{{100}} cr
& = { ext{Rs}}{ ext{. }}408 cr} $$ After transportation charges cost price $$eqalign{
& = 408 + 28{ ext{ }} cr
& { ext{ = Rs}}{ ext{. 436}} cr
& { ext{Gain }}\% cr
& = frac{{545 - 436}}{{436}} imes 100\% cr
& = frac{{109}}{{436}} imes 100\% cr
& = 25\% cr} $$