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.

Answer:

Marked Price = 16450 Rs.

Off season discount = 16 \%

Discount = \frac{16}{100} \times Market Price 

= \frac{16}{100} \times 16450

= 2632 Rs.

= 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.

Answer:

Market Price of the sweater = 850 Rs.

Selling Price= 731 Rs.

Discount = Marked Price - Selling Price

= 850 - 731 = 119 Rs.

\\

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.

Answer:

Selling Price of a mini toy gun = 345 Rs.

Discount = 30 Rs.

Marked Price = Selling Price + Discount

= 345 + 30 = 375 Rs.

\\

Question 4: 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 = 1156 Rs.

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 ( \frac{1156 \times 100}{85} ) = 1360

Marked Price of the body Suit = 1360 Rs.

\\

Question 5: 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 = 435 Rs.

Discount = 13 \% on the marked price

Let Marked Price = x Rs.

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 = 500 Rs.

\\

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.

Answer:

Let Cost Price = x Rs.

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

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

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 \%

\\

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.

Answer:

The cost price = 7660 Rs.

Let M.P. = x Rs.

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 = ( \frac{8426 \times 100}{88} ) = 9575 Rs.

\\

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.

Answer:

Cost of the sewing machine = 3750 Rs.

Let Mark Price. = x Rs.

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)      … … … … … i)

Gain is 26 \% of the CP = \frac{26}{100} \times 3750 = 975      … … … … … ii)

Equating i) and ii)

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

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

Marked Price = 5250 Rs.

\\

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?

Answer:

Let Marked Price = x Rs.

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?

Answer:

Let marked price in x Rs. 

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 \%

Answer:

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

1^{st} Discount is 20 \% , Discount = 20 Rs. 

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

2^{nd} discount is 10 \% of  80 = \frac{10}{100} \times 80 = 8 Rs.

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

S.P. of the article 72 Rs. 

Net discount =  100 -  72 = 28 Rs. 

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

Single discount equivalent to given successive discounts = 28 \%

\\

Question 13: 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 \ 100 = 40 Rs.

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

Next Discount is = 5 \% \ of \ 60

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

Price after second Discount = 60-3 =  57 Rs.

That is S.P. = 57 Rs. 

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

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

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

\\

Question 14: 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 100 = 20 Rs.

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

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

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

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

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

S.P. of the article = 75.24 Rs.

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

Single discount equivalent to given successive discounts = 24.76 \%