Practice Discount: True and Banker's

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Calculate Discount if,

Market Price \[(MP) = Rs.100\]
Selling Price \[(SP) = Rs.200\]

\[Rs.50\]

\[Rs.100\]

\[Rs.150\]

\[Rs.200\]

Discount \[= SP - MP\]

\[=200-100\]

\[=Rs.100\]

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Calculate Net Loss if,

Cost Price \[(CP) = Rs.100\]
Selling Price \[(SP) = Rs.50\]

\[Rs.20\]

\[Rs.50\]

\[Rs.100\]

\[Rs.150\]

Net Loss \[= CP - SP\]

\[=100-50\]

\[=Rs.50\]

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Calculate Discount (in percentage \[\%\]) if,

Market Price \[(MP) = Rs.50\]
Selling Price \[(SP) = Rs.60\]

\[5\%\]

\[10\%\]

\[15\%\]

\[20\%\]

Discount \[\% = \frac{SP - MP}{MP}\times100\]

\[=\left(\frac{60-50}{50}\times 100\right)\%\]

\[=\left(\frac{10}{50}\times 100\right)\%\]

\[=\left(\frac{1}{5}\times 100\right)\%\]

\[=20\%\]

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Calculate Net Loss (in percentage \[\%\]) if,

Selling Price \[(CP) = Rs.100\]
Cost Price \[(SP) = Rs.200\]

\[20\%\]

\[30\%\]

\[40\%\]

\[50\%\]

Net Loss \[\% = \frac{CP - SP}{CP}\times100\]

\[=\left(\frac{200-100}{200}\times 100\right)\%\]

\[=\left(\frac{100}{200}\times 100\right)\%\]

\[=\left(\frac{1}{2}\times 100\right)\%\]

\[=50\%\]

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Successive discounts of \[10\%\] and \[20\%\] are equivalent to a single discount of :

\[22\%\]

\[24\%\]

\[26\%\]

\[28\%\]

Equivalent discount of successive discounts of \[10\%\] and \[20\%\]

\[=\left(10+20-\frac{\left(10\times 20\right)}{100}\right)\%\]

\[=\left(30-\frac{200}{100}\right)\%\]

\[=\left(30-2\right)\%\]

\[=28\%\]

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A single discount equivalent to the successive discounts of \[10\%\], \[20\%\] and \[25\%\] is

\[40\%\]

\[42\%\]

\[44\%\]

\[46\%\]

This question will be solved in two parts :

Part - 1

Calculating Single of discount for successive discounts 10% and 20%

\[=\left(10+20-\frac{\left(10\times 20\right)}{100}\right)\%\]

\[=\left(30-\frac{200}{100}\right)\%\]

\[=\left(30-2\right)\%\]

\[=28\%\]

Part - 2

Calcuating Single of discount for successive discounts 28% and 25%

\[=\left(28+25-\frac{\left(28\times 25\right)}{100}\right)\%\]

\[=\left(53-\frac{28}{4}\right)\%\]

\[=\left(53-7\right)\%\]

\[=46\%\]

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What price should a shopkeeper mark on an article costing him \[Rs.200\] to gain \[50\%\].

\[Rs.100\]

\[Rs.200\]

\[Rs.300\]

\[Rs.400\]

CP \[= Rs.200\]

Gain \[= 50\%\]

\[\therefore\] Selling Price

\[=\frac{CP\times \left(100+Gain\%\right)}{100}\]

\[=\frac{200\times \left(100+50\right)}{100}\]

\[=\frac{200\times \left(150\right)}{100}\]

\[=2\times 150\]

\[=300\]

Hence, selling price \[=Rs.300/-\]

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A shopkeeper sells an item in \[Rs.210\] to gain \[5\%\]. Find the Cost Price?

\[Rs.180\]

\[Rs.190\]

\[Rs.200\]

\[Rs.210\]

Let the Cost Price \[(CP) = x\],

Then, According to the question

\[SP = (100+5)\% \ of\ CP\]

\[210=\frac{105}{100}\times x\Rightarrow x\]

\[=\frac{\left(210\times 100\right)}{105}\]

\[=2\times 100\]

\[=200\]

Hence, the Cost Price \[(CP)=Rs.200/-\]

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If \[10\%, 20\%, 30\%\] are successive discounts, then equivalent discount is

\[34.2\%\]

\[45.4\%\]

\[49.6\%\]

\[50.4\%\]

If \[\left(D_1,D_2,D_3\right)\] are successive discounts, then equivalent discount/overall discount is (in percentage)

\[=100-\left[\left(\frac{100-D_1}{100}\right)\left(\frac{100-D_2}{100}\right)\left(\frac{100-D_3}{100}\right)\times 100\right]\]

\[\therefore\] Equivalent Discount

\[=100-\left[\left(\frac{100-10}{100}\right)\left(\frac{100-20}{100}\right)\left(\frac{100-30}{100}\right)\times 100\right]\]

\[=100-\left[\left(\frac{90}{100}\right)\left(\frac{80}{100}\right)\left(\frac{70}{100}\right)\times 100\right]\]

\[=100-\left[\left(\frac{9}{10}\right)\left(\frac{8}{10}\right)\left(\frac{7}{10}\right)\times 100\right]\]

\[=100-\left[\left(\frac{9\times 8\times 7}{1000}\right)\times 100\right]\]

\[=100-\left(\frac{9\times 8\times 7}{10}\right)\]

\[=100-\left(\frac{504}{10}\right)\]

\[=100-50.4\]

\[=49.6\%\]

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Single equivalent discount for \[x\%\] and \[y\%\] is

\[\left(x+y-\frac{xy}{100}\right)\%\]

\[\left(x+y+\frac{xy}{100}\right)\%\]

\[\left(-x+y-\frac{xy}{100}\right)\%\]

\[\left(-x+y+\frac{xy}{100}\right)\%\]

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Calculate Discount \[\%\] if,

Discount \[= Rs.10\]
Market Price \[(MP) = Rs.40\]

\[10\%\]

\[15\%\]

\[20\%\]

\[25\%\]

\[Discount\ \%=\frac{Discount}{MP}\times 100\]

\[=\frac{10}{40}\times 100\]

\[=\frac{1}{4}\times 100\]

\[=25\%\]

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Calculate Selling Price \[(SP)\] if,

Discount \[ = 5\%\]
Market Price \[(MP) = Rs.1000\]

\[Rs.800\]

\[Rs.850\]

\[Rs.900\]

\[Rs.950\]

\[SP=\frac{MP\left(100-D\right)}{100}\]

\[=\frac{1000\left(100-5\right)}{100}\]

\[=10\times 95\]

\[=950\]

Hence, Selling Price \[(SP)=Rs.950/-\]

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Calculate Market Price \[(MP)\] if,

Discount \[ = 20\%\]
Selling Price \[(SP) = Rs.1600\]

\[Rs.1400\]

\[Rs.1600\]

\[Rs.1800\]

\[Rs.2000\]

\[MP=\frac{SP\times 100}{100-D}\]

\[=\frac{1600\times 100}{100-20}\]

\[=\frac{1600\times 100}{80}\]

\[=20\times 100\]

\[=2000\]

Hence, Market Price \[(MP)=Rs.2000/-\]

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\[2\] articles are given free on purchasing \[5\] articles. Then, Discount % is _________

\[10\%\]

\[20\%\]

\[30\%\]

\[40\%\]

‘y’ articles (quantity/number) are given free on purchasing ‘x’ articles. Then, Discount %

\[=\left(\frac{y\times 100}{x+y}\right)\%\]

\[\therefore Discount\]

\[=\frac{\left(2\times 100\right)}{2+8}\]

\[=\frac{\left(2\times 100\right)}{10}\]

\[=\frac{200}{10}\]

\[=20\%\]

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A tradesman marks his goods \[3\%\] above his cost price. If he allows his customers a discount of \[2\%\] on the marked price. how much profit or loss does he make, if any ?

\[0.7\%\] Profit

\[0.7\%\] Loss

\[0.9\%\] Profit

\[0.9\%\] Loss

A tradesman marks his goods \[r_1\%\] above his cost price. If he allows his customers a discount of \[r_2\%\] on the marked price. Then his profit or loss percent is

\[\frac{r_1\times \left(100-r_2\right)}{100}-r_2\]

Hence Profit or Loss %

\[=\frac{3\times \left(100-2\right)}{100}-2\]

\[=\frac{3\times 90}{100}-2\]

\[=\frac{270}{100}-2\]

\[=2.7-2\]

\[=0.7\%\]

Positive sign signifies profit of \[0.7\%\]

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A tradesman marks his goods \[4\%\] above his cost price. If he allows his customers a discount of \[5\%\] on the marked price. how much profit or loss does he make, if any ?

\[1.2\%\] Profit

\[1.4\%\] Loss

\[1.6\%\] Profit

\[1.8\%\] Loss

A tradesman marks his goods \[r_1\%\] above his cost price. If he allows his customers a discount of \[r_2\%\] on the marked price. Then his profit or loss percent is

\[\frac{r_1\times \left(100-r_2\right)}{100}-r_2\]

Hence Profit or Loss %

\[=\frac{4\times \left(100-5\right)}{100}-5\]

\[=\frac{4\times 90}{100}-5\]

\[=\frac{360}{100}-5\]

\[=3.6-5\]

\[=-1.4\%\]

Negative sign signifies Loss of \[1.4 \%\]

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Successive discounts of \[20\%\] and \[10\%\] are given on an item marked at \[Rs. 700\]. Find the selling price.

\[Rs.401\]

\[Rs.504\]

\[Rs.603\]

\[Rs.704\]

Required selling price

\[=Rs.\left[700\times \frac{(100-20)}{100}\times \frac{(100-10)}{100}\right]\]

\[=Rs.\left[700\times \frac{80}{100}\times \frac{90}{100}\right]\]

\[=Rs.504\]

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A trader marked the selling price of an article at \[10\%\] above the cost price. At the time of selling, he allows certain discount and suffers a loss of \[1\%\]. He allowed the discount of :

\[10\%\]

\[15\%\]

\[20\%\]

\[25\%\]

Let C.P. be \[100\]

Marked price \[= 110\]

\[\therefore x\%\ of\ 110=11\]

\[\Rightarrow x=\frac{\left(11\times 100\right)}{110}\]

\[=10\%\]

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A seller marks his goods \[30\%\] above their cost price but allows \[15\%\] discount for cash payment. His percentage of profit when sold in cash is

\[10\%\]

\[10.5\%\]

\[11\%\]

\[11.5\%\]

Let the C.P. be \[100\]

\[\therefore\] Marked price \[= 130\]

S.P. \[= 85 \% \ of \ 130\]

\[=Rs.\left(\frac{85\times 130}{100}\right)\]

\[=Rs.110.5\]

\[\therefore\] Gain percent \[= 10.5\%\]

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A trader marks his goods \[45\%\] above the cost price and gives a discount of \[20\%\] on the marked price. The gain \[%\] on goods he makes is :

\[10\%\]

\[12\%\]

\[14\%\]

\[16\%\]

Let the C.P. of article be \[100 \]

\[\implies\] Marked price \[= 145\]

\[\Rightarrow\] SP \[=\frac{145\times 80}{100}\]

\[=Rs.116\]

\[\implies\] Profit percent \[=116\%\]