Question 1:  The marked price of a refrigerator is Rs.16450. The shopkeeper offers on off-season discount of 16% on it. Find its selling price.

$Marked\ Price\ =Rs.16450$

$Off\ season\ discount\ =16\%$

$Discount\ =\ Rs.\frac{16}{100}\times{}Market\ Price$

$=\ Rs.\frac{16}{100}\times{}16450$

$=\ Rs.2632$

$=\ 16450-2632\ =\ 13818\ Rs.$

Question 2:  The price of a sweater was slashed down by a shopkeeper from Rs.850 to Rs.731. Find the rate of discount given by him.

$Market\ Price\ of\ the\ sweater\ =\ Rs.850$

$Selling\ Price=Rs.731$

$Discount\ =\ Marked\ Price-Selling\ Price$

$\ \ \ \ =\ Rs.850-Rs.\ 731$

$\ \ \ \ =\ Rs.119$

Question 3:  Find the rate of discount being given on mini toy-gun whose selling price is Rs.345 after deducting a discount being given on a mini toy-gun whose selling price is Rs. 345 after deducting a discount of Rs.30 on its marked price.

$Selling\ Price\ of\ a\ mini\ toy\ gun\ =Rs.345$

$Discount\ =\ Rs.30$

$Marked\ Price\ \ \ =\ Selling\ Price\ +\ Discount$

$=\ Rs.345\ +\ Rs.30$

$=\ Rs.375$

Question 4:  After allowing a   discount of 15%, a baby-suit was sold for Rs.1156.find its marked price.

$Selling\ Price\ of\ a\ baby\ suit=Rs.\ 1156$

$Discount\ =\ 15\%$

$Let\ Marked\ Price\ \ =\ Rs.\ x$

$Discount\ =\frac{15}{100}\times{}x$

$Selling\ Price = x - \frac{15x}{100} = \frac{85}{100} x$

Equating the above with actual selling price

$\frac{85}{100}x\ =\ 1156$

$x\left(\ \ \frac{1156\ \times{}100}{85}\right)=1360$

$Marked\ Price\ of\ the\ body\ Suit\ =\ Rs.1360$

Question 5:  A calculator was bought for Rs.435 after getting a discount of 13%. Find the marked price of the calculator.

$Purchase\ Price\ of\ the\ calculator=Selling\ Price\ of\ the\ calculator \\ =Rs.\ 435$

$Discount\ =13\%\ on\ the\ marked\ \ price$

$Let\ Marked\ Price\ =Rs.\ x$

$Discount\ =\ \frac{13}{100}x$

$M.P.\ =\ S.P.\ +\ Discount$

$x=\ 435+\frac{13}{100}x$

$or\ x\ -\ \frac{13}{100}x=435$

$or\ \ \frac{87}{100}x=435$

$or\ x\ =\ \ \frac{435\ \times{}100}{87}=500$

$Marked\ price\ of\ the\ calculate\ =Rs.500$

Question 6:  A dealer marked his goods 35% above cost price and allowed a discount of 20% on the market price. Find his gain or loss per cent.

$Let\ Cost\ Price\ =\ Rs.x$

$Marked\ Price\ =\ x\ +\frac{35}{100}x =\ \frac{135}{100}x$

$Discount\ =\ 20\%\ on\ M.P. =\ \left(\frac{20}{100}\right)\ \times{}M.P.\ =\ \left(\frac{20}{100}\right)\ \times{}\left(\frac{135}{100}\right)x$

$S.P.\ \ \ =\ M.P.-\ Discount =\ \frac{135}{100}x-\frac{20}{100}\times{}\frac{135}{100}x =\ \frac{80}{100}\times{}\frac{135}{100}x$

$Profit = S.P. - Cost\ Price =\ \frac{80\times{}135}{100\times{}100}x-x = 1.08x - x =0.08\ x$

$\%\ age\ profit\ =\ \frac{Profit}{C.P.}\times{}100 =\ \frac{0.08x}{x}\times{}100=8\%$

Question 7:  An article was marked 40% above cost price and a discount of 35% was given on its marked price. Find the gain or loss per cent made by the shopkeeper.

$Let\ Cost\ Price\ =\ Rs.\ x$

$Marked\ Price\ =\ x\ +\ \frac{40}{100}x=\ \frac{140}{100}x$

$Discount\ =\ 35\%\ of\ the\ M.P.=\ \frac{35}{100}\times{}\frac{140}{100}x$

$S.P. = M.P. - Discount = \frac{140x}{100} -\frac{35}{100} \times {} \frac{140}{100}x = \frac{65}{100} \times{} \frac{140}{100}x$

$Gain = Cost - S.P. = x - \frac{65}{100} \times \frac{140}{100} x = x - 0.91 x = 0.09x$

$\ \%\ \ Gain\ \ =\frac{0.09x}{x}\times{}100=\ 9\%$

Question 8:  A dealer purchased a washing machine for Rs.7660. after allowing a discount of 12% on its marked price, he gains 10%. Find the marked price.

$The\ cost\ price\ =\ Rs.7660$

$Let\ M.P.\ =\ Rs.\ x$

$Discount\ =\ \frac{12}{100}$

$S.P. = M.P. - Discount =\ Rs.x\ -\frac{12}{100}x =\ Rs.\ \frac{88}{100}x$

$\ Gain\ is\ 10\%\ of\ the\ cost\ Price =Rs.\ \frac{10}{100}\times{}7660=\ Rs.\ 766$

$Gain = S.P. - Cost Price =\frac{88}{100}x - 7660$

$766\ =\ \frac{88}{100}x-7660$

$\ \frac{88}{100}x=7660+766\ =\ 8426$

$x\ =\ Rs.\left(\ \frac{8426\ \times{}100}{88}\right)\ =\ Rs.9575$

Question 9:  A shopkeeper bought a sewing machine for Rs.3750. after allowing a discount of 10% on its marked price, he gains 26%. Find the marked price of the sewing machine.

$Cost\ of\ the\ sewing\ machine\ =\ Rs.3750$

$Let\ Mark\ Price.\ =\ Rs.\ x$

$Discount\ =\ \frac{10}{100}x$

$Selling\ Price\ = x - \frac{10}{100}x =\ \frac{90}{100}x$

$Gain = Selling \ Price - Cost \ Price = (\frac{90}{100}x - 3750) ...eq(1)$

$Gain\ is\ 26\%\ of\ the\ CP =\ \frac{26}{100} \times 3750 = 975 ...eq(2)$

$Equating\ 1)\ and\ 2)$

$\frac{90}{100}x-3750=975$

$or \ \ x\ =\ (975\ +3750)\ \times{}\frac{100}{90}\ =\ 5250$

$Marked\ Price\ =\ Rs.\ 5250$

Question 10:  After allowing a discount of 10% on the marked price, a trader still makes a profit of 17%. By what per cent is the marked price above cost price?

$Let\ Marked\ Price\ =\ Rs.\ x$

$S.P.\ =\ x \ - \ Discount \ of \ 10 \% \ of \ x =\ x-\frac{10}{100}x =\ \frac{90}{100}x$

$\%\ Gain\ =\ \frac{S.P-C.P}{C.P}\times{}x$

$(\%gain)(C.P.)= S.P.\times 100 - C.P.\times 100$

$\ (\%\ \ gain)\ (C.P.)\ +C.P.\ \times{}100=S.P.100$

$C.P.\ =\ \frac{S.P.\ \times{}100}{\%\ gain\ +100} =\ \frac{x\frac{90}{100}\times{}100}{17+100}=\ \frac{90}{117}x$

$Difference\ between\ M.P.\ and\ C.P. =x - \frac{90}{117}x = \frac{27}{117}x$

$\%age\ of\ difference\ in\ marked\ price\ over\ cost\ price\ \\ =\ \frac{\frac{27}{117}x}{\frac{90}{117}x}\times{}100\ =\ 30\%$

Question 11:  After allowing a discount of 12% on the marked price, a shopkeeper still gains 21%. By what per cent is the marked price above cost price?

$Let\ marked\ price\ in\ Rs.\ x$

$S.P.\ =\ x-12\%\ discount\ on\ x =x\ -\frac{12}{100}x =\ \frac{88}{100}x$

$C.P.\ =\ \frac{S.P.\ \times{}100}{\%\ \ gain\ +100}=\frac{\frac{88}{100}x\times{}100}{21+100}=\frac{88}{121}x$

$Difference\ between\ M.P.\ and\ C.P. =x\ \ -\frac{88}{121}x =\ \frac{33}{121}x$

$\%\ of\ difference\ in\ marked\ price\ over\ cost\ price \\ =\ \frac{\frac{33}{121}x}{\frac{88}{121}x}\times{}100 =\ \frac{300}{8}=37.5\%$

Question 12:  Find a single discount equivalent to two successive discounts of 20% and 10%

$\ Let\ the\ M.P. \ of \ the \ article \ be \ Rs.\ 100$

$Ist \ Discount\ is \ 20\%,\ Discount\ = Rs. \ 20$

$Reduced \ Price \ after \ the \ first\ discount\ = \ Rs.\ (100-20)\ =\ Rs. \ 80$

$Second\ discount\ is \ 10\% \ of Rs.\ 80\ = \ \frac{10}{100} \times 80 \ =\ Rs.\ 8$

$Price\ after \ the \ second\ discount \ = Rs.\ 80 - Rs.\ 8 = Rs.\ 72$

$S.P.\ of\ the\ article\ Rs.\ 72$

$Net\ discount\ = \ Rs.\ 100 - Rs.\ 72 = Rs.\ 28$

$Thus,\ net\ discount \ on \ M.P.\ of\ Rs.\ 100 \ is \ Rs.\ 28$

$Single \ discount\ equivalent\ to \ given \ successive \ discounts = Rs.28\%$

Question 13:  Find a single discount equivalent to two successive discounts of 40% and 5%.

$Let\ the \ M.P. \ of \ an \ article \ is \ Rs.\ 100$

$Discount \ on \ it \ is \ =\ 40\% \ of \ Rs.\ 100 = Rs.\ 40$

$Reduced \ Price \ after \ first\ discount\ = \ Rs.(100-40)\ =\ Rs.\ 60$

$Next\ Discount \ is \ =5\% \ of \ Rs.\ 60$

$Rs. (\frac{5}{100} \times 60) = Rs. 3$

$Price \ after \ second\ Discount \ = \ Rs.\ (60-3)=Rs.\ 57$

$That \ is \ S.P. \ = \ Rs.\ 57$

$Net\ Discount\ = \ M.P. \ -S.P.\ = \ Rs.\ 100 -57\ =\ Rs.\ 43$

$Thus, \ net\ discount\ on\ MP. \ of\ Rs.\ 100 \ is \ Rs.\ 43.$

$Single \ discount \ equivalent \ to \ given \ successive \ discounts \ =\ 43\%$

Question 14:  Find a single discount equivalent to three successive discounts of 20%, 5% and 1%

$Let\ the \ M.P. \ of\ an \ article \ in \ Rs.\ 100$

$It \ discount \ on \ it \ is \ = \ 20\% \ of \ Rs.\ 100 \ =\ Rs.\ 20$

$Reduced\ price \ after \ the \ its\ discount \ = \ Rs.100\ -\ 20\ =\ Rs.\ 80$

$Second \ discount \ on\ it\ =\ 5%\ of \ Rs\ .80\ = \frac{5}{100} \times 80 =Rs.4$

$Price\ after \ second \ discount \ = Rs.\ 80-4=Rs.\ 76$

$Third\ discount \ on \ it \ is \ 1\% \ of \ Rs.\ 76 = \frac{1}{100} \times 76=0.76$

$Price \ after \ Third \ discount \ = \ Rs.\ 76-0.76 \ = \ Rs.\ 75.24$

$S.P. \ of\ the \ article \ =\ Rs.\ 75.24$

$Thus, \ net \ discount \ on \ M.P. \ of \ Rs.100\ in \ Rs.\ 24.76$

$Single \ discount\ equivalent \ to\ given \ successive \ discounts \ =\ 24.76%$