Q1. The marked price of a refrigerator is Rs.16450. The shopkeeper offers on off-season discount of 16% on it. Find its selling price.

Answer:

   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.  

 

Q2. 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.

Answer:

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

   Selling\ Price=Rs.731  

   Discount\ =\ Marked\ Price-Selling\ Price  

   \ \ \ \ =\ Rs.850-Rs.\ 731  

   \ \ \ \ =\ Rs.119  

 

Q3. 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.

Answer:

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

   Discount\ =\ Rs.30  

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

   =\ Rs.345\ +\ Rs.30  

   =\ Rs.375  

 

Q4. After allowing a   discount of 15%, a baby-suit was sold for Rs.1156.find its marked price.

Answer:

   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  

 

Q5. A calculator was bought for Rs.435 after getting a discount of 13%. Find the marked price of the calculator.

Answer:

   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  

 

Q6. 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.

Answer:

   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\%  

 

Q7. 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.

Answer:

  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\% 

 

Q8. 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.

Answer:

  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 

 

Q9. 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.

Answer:

 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  

 

Q10. 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?

Answer:

 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\%   

 

Q11. 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?

Answer:

 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\%   

 

Q12. Find a single discount equivalent to two successive discounts of 20% and 10%

Answer:

\  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\%   

 

Q13. Find a single discount equivalent to two successive discounts of 40% and 5%.

Answer:

 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\%   

 

Q14. Find a single discount equivalent to three successive discounts of 20%, 5% and 1%

Answer:

 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% 

Advertisements