True Discount - Study Mode

[#76] Two successive discounts of 10% and 5%, in this order, are given on a bill of Rs. 110. Find the net amount of money payable to clear the bill (answer to the nearest rupee) = ?
Correct Answer

(A) Rs. 94

Explanation

Solution: Bill amount = Rs. 110 After discount net amount of Bill 90% of 95% of 110 $$eqalign{
& frac{{90}}{{100}} imes frac{{95}}{{100}} imes 110 cr
& { ext{ = Rs}}{ ext{. 94 ( approx )}} cr} $$

[#77] A merchant allows a discount of 10% on marked price for the cash payment. To make a profit of 17%, he must mark his goods higher than their cost price by = ?
Correct Answer

(D) 30%

Explanation

Solution: $$eqalign{
& { ext{Let the cost price = Rs}}{ ext{. 100}} cr
& { ext{Selling price }} cr
& { ext{ = 117}}\% { ext{ of 100 }} cr
& { ext{ = Rs}}{ ext{. 117}} cr
& { ext{Marked price}} cr
& { ext{ = 117}} imes frac{{100}}{{90}}{ ext{ }} cr
& { ext{ = Rs}}{ ext{. 130}} cr
& { ext{Marked price above }}\% cr
& = frac{{130 - 100}}{{100}} imes 100\% cr
& = 30\% cr} $$

[#78] The total discount on Rs.1860 due after a certain time at 5% is Rs. 60. Find the time after which it is due -
Correct Answer

(D) 8 months

Explanation

Solution: $$eqalign{
& { ext{Here, A}}, = ,1860, cr
& { ext{R}}, = ,5\% cr
& { ext{TD}}, = 60 cr
& herefore ,{ ext{TD}}, = ,frac{{A imes R imes T}}{{100 + R imes T}} cr
& Rightarrow 60 = frac{{1860 imes 5 imes T}}{{100 + 5T}} cr
& Rightarrow 6000 + 300T = 9300T cr
& Rightarrow 6000 = 9300T - 300T cr
& Rightarrow 6000 = 9000T cr
& Rightarrow T = frac{{6000}}{{9000}} cr
& Rightarrow T, = frac{2}{3}{ ext{year}} cr
& Rightarrow T, = frac{2}{3} imes 12 cr
& Rightarrow T = 8,{ ext{months}} cr} $$

[#79] If the discount is equal to one fifth of the marked price and the loss is half the discount, then the percentage of loss is = ?
Correct Answer

(B) $$11frac{1}{9}\% $$

Explanation

Solution: Let the marked price = Rs. 100 $$eqalign{
& { ext{Discount}} = frac{1}{5} imes 100 cr
& ,,,,,,,,,,,,,,,,,,,,,,, = { ext{Rs}}{ ext{. }}20 cr
& { ext{Loss = }}frac{1}{2} imes 20 cr
& ,,,,,,,,,,{ ext{ = Rs}}{ ext{. 10}} cr
& { ext{Cost price}} = 100 - 20 + 10 cr
& ,,,,,,,,,,,,,,,,,,,,,,,,{ ext{ = Rs}}{ ext{. 90}} cr
& { ext{Loss}}\% = frac{{10}}{{90}} imes 100 cr
& ,,,,,,,,,,,,,, = frac{{100}}{9}\% { ext{ }} cr
& ,,,,,,,,,,,,,, = 11frac{1}{9}\% { ext{ }} cr} $$

[#80] How much percent more than the cost price should a shopkeeper mark his goods so that after allowing a discount of 25% on the marked price, he gain 20% ?
Correct Answer

(C) 60%

Explanation

Solution: $$eqalign{
& { ext{Let the cost price = Rs}}{ ext{. 100}} cr
& { ext{Selling price = 120}}\% { ext{ of 100}} cr
& ,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,{ ext{ = Rs}}{ ext{. 120}} cr
& { ext{Market price = 120}} imes frac{{100}}{{75}}{ ext{ }} cr
& ,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,{ ext{ = Rs}}{ ext{. 160}} cr
& { ext{Above }}\% { ext{ = }}frac{{160 - 100}}{{100}} imes 100 cr
& ,,,,,,,,,,,,,,,,,,,,,,,, = 60\% cr} $$