Class 8: Profit and Loss – Exercise 14C – ICSE / ISC / CBSE Mathematics Portal for K12 Students

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.

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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.

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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.

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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.

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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.

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

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

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

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

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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.

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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.

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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 $\ = \$ $\frac{\frac{27}{117}x}{\frac{90}{117}x}$ $\times 100 = 30 \%$

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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 $\ =$ $\frac{\frac{33}{121}x}{\frac{88}{121}x}$ $\times 100 =$ $\frac{300}{8}$ $= 37.5 \%$

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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 $= 28 \%$

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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 \% $

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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 $= 24.76 \%$

ICSE / ISC / CBSE Mathematics Portal for K12 Students

Mathematics Made Easy for School Students

Class 8: Profit and Loss – Exercise 14C

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