Question

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Math question

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A bicycle was sold at the profit of 12% Had it been sold for Rs.16 more the profit would have been 20% . Find the selling price of the bicycle.

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Topic : Profit and Loss

Answer 1

$\textsf{Let the Selling Price of the Bicycle be : SP}$

$\textsf{Let the Cost Price of the Bicycle be : CP}$

$\sf{Given : If\;the\;Bicycle\;is\;sold\;at\;the\;Selling\;Price\;(SP),\;Profit\;Percentage\;is\;12\%}$

$\sf{\bigstar\;\;We\;know\;that : \sf{Profit\;Percentage = {\bigg(\dfrac{SP - CP}{CP}\bigg)\times 100}}$

$\sf{\implies {\bigg(\dfrac{SP - CP}{CP}\bigg)\times 100} = 12}$

$\sf{\implies {\bigg(\dfrac{SP}{CP} - 1\bigg) \times 100} = 12\;------\;[1]}$

$\textsf{Given : If Bicycle is sold for Rs.16 more the Profit would be 20\%}$

$\implies \textsf{New Selling Price which made 20\% will be : (SP + 16)}$

$\sf{\implies \bigg(\dfrac{SP + 16 - CP}{CP}\bigg)\times 100 = 20}$

$\sf{\implies {\bigg(\dfrac{SP}{CP} + \dfrac{16}{CP} - 1 \bigg)\times 100} = 20}$

$\sf{\implies {\bigg(\dfrac{SP}{CP} - 1 \bigg)\times 100} + \bigg(\dfrac{16}{CP}\bigg) \times 100 = 20}$

$\textsf{Substituting the Value of Equation [1] in the above Equation, We get :}$

$\sf{\implies 12 + \bigg(\dfrac{16}{CP}\bigg) \times 100 = 20}$

$\sf{\implies \bigg(\dfrac{16}{CP}\bigg) \times 100 = 20 - 12}$

$\sf{\implies \bigg(\dfrac{16}{CP}\bigg) \times 100 = 8}$

$\sf{\implies 1600 = 8CP}$

$\sf{\implies CP = \dfrac{1600}{8}}$

$\sf{\implies CP = 200}$

$\textsf{Substituting the Value of CP in Equation [1], We get :}$

$\sf{\implies \bigg(\dfrac{SP}{200} - 1\bigg)\times 100 = 12}$

$\sf{\implies \dfrac{100(SP)}{200} - 100 = 12}$

$\sf{\implies \dfrac{(SP)}{2} = 100 + 12}$

$\sf{\implies \dfrac{(SP)}{2} = 112}$

$\sf{\implies SP = 112 \times 2}$

$\implies \sf{SP = 224}$

$\bf{Answer : }\;\;\textsf{The Selling Price of the Bicycle is Rs.224}$

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$\sf{\underline{Method - 2}}$

$\textsf{Let the Selling Price of the Bicycle be : SP}$

$\textsf{Let the Cost Price of the Bicycle be : CP}$

$\sf{Given : If\;the\;Bicycle\;is\;sold\;at\;the\;Selling\;Price\;(SP),\;Profit\;Percentage\;is\;12\%}$

$\sf{\implies {\bigg(\dfrac{SP - CP}{CP}\bigg)\times 100} = 12}$

$\sf{\implies {\bigg(\dfrac{SP - CP}{CP}\bigg)} = \dfrac{12}{100}}$

$\sf{\implies {\bigg(\dfrac{SP}{CP} - 1\bigg)} = 0.12}$

$\sf{\implies {\dfrac{SP}{CP}} = 1 + 0.12}$

$\sf{\implies {\dfrac{SP}{CP}} = 1.12}$

$\implies \sf{SP = 1.12CP\;------\;[1]}$

$\textsf{Given : If Bicycle is sold for Rs.16 more the Profit would be 20\%}$

$\implies \textsf{New Selling Price which made 20\% will be : (SP + 16)}$

$\sf{\implies \bigg(\dfrac{SP + 16 - CP}{CP}\bigg)\times 100 = 20}$

$\sf{\implies \bigg(\dfrac{1.12CP + 16 - CP}{CP}\bigg) = \dfrac{20}{100}}$

$\sf{\implies \bigg(\dfrac{0.12CP + 16}{CP}\bigg) = 0.2}$

$\sf{\implies 0.12 + \dfrac{16}{CP} = 0.2}$

$\sf{\implies \dfrac{16}{CP} = 0.08}$

$\sf{\implies CP = \dfrac{16}{0.08}}$

$\sf{\implies CP = 200}$

$\textsf{Substituting the Value of CP in Equation [1], We get :}$

$\sf{\implies SP = 1.12 \times 200}$

$\sf{\implies SP = 224}$

$\textsf{The Selling Price of the Bicycle is Rs.224}$

Answer 2

Let CP of Bicycle be=₹x
SP=12% Profit
$sp = x + (x \times 12\%) \\ = x + (x \times \frac{12}{100} ) \\ = x + \frac{3x}{25} \\ = \frac{25x + 3x}{25} \\ = \frac{28x}{25}$

SP=₹28x/25
CP=₹x
If ₹16 more on CP Profit=20%
A/Q
$x + (x \times 20\%) = \frac{28x}{25} + 16 \\ = x + (x \times \frac{20}{100} ) = \frac{28x + 16 \times 25}{25} \\ = x + \frac{x}{5} = \frac{28x}{25} + \frac{400}{25} \\ = \frac{5x + x}{5} - \frac{28x}{25} = \frac{400}{25} \\ = \frac{6x}{5} - \frac{28x}{25} = 16 \\ = \frac{30x - 28x}{25} = 16 \\ = \frac{2x}{25} = 16 \\ = x = 16 \times \frac{25}{2} \\ x = 200$
CP=₹200
SP=28×200/25
=₹224
SP when 12% profit=₹224
SP when 20% profit=₹240