Question

if artical is sold at a certain price one gains 10%.what will be the gain percent if sold for double the price?​

Answer 1

$\\\;\underbrace{\underline{\sf{Understanding\;the\;Question}}}$

Here the Concept of Gain Percent has been used. We are given that a person gains a percentage on selling an article. Now we can take the Cost Price as a constant and then by adding gain% we can find the selling price. After finding that we get the new selling price by doubling and then again we can find the final gain%.

Let's do it !!

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★ Formula Used :

$\\\;\boxed{\sf{\pink{SP\;=\;\bf{\dfrac{100\;+\;gain\%}{100}\:\times\:CP}}}}$

$\\\;\boxed{\sf{\pink{Gain\;=\;\bf{SP\;-\;CP}}}}$

$\\\;\boxed{\sf{\pink{Gain\%\;=\;\bf{\dfrac{Gain}{100}\;\times\;CP}}}}$

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★ Solution :-

Given,

» Initial Gain % = 10 %

» Selling Price is denoted by 'SP'

» Cost Price is denoted by 'CP'

• Let the Cost Price of the Article be Rs. 100

From this we can find the Initial Selling Price. This can be given as,

$\\\;\sf{:\rightarrow\;\;SP_{(Initial)}\;=\;\bf{\dfrac{100\;+\;gain\%}{100}\:\times\:CP}}$

$\\\;\sf{:\rightarrow\;\;SP_{(Initial)}\;=\;\bf{\dfrac{100\;+\;10}{100}\:\times\:100}}$

$\\\;\sf{:\rightarrow\;\;SP_{(Initial)}\;=\;\bf{\dfrac{110}{100}\:\times\:100}}$

$\\\;\sf{:\rightarrow\;\;SP_{(Initial)}\;=\;\bf{\orange{Rs.\;110}}}$

Hence, Initial Selling Price = Rs. 110

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~ For the New Gain % ::

Its given that the selling price is doubled that is article is sold in double price. This can give as,

$\\\;\bf{\mapsto\;\;SP_{(Final)}\;=\;\bf{2\:\times\:110}}$

$\\\;\bf{\mapsto\;\;SP_{(Final)}\;=\;\bf{\red{Rs.\;220}}}$

This is the new final Selling price that is Rs. 200

Now New Gain is given as,

$\\\;\sf{\rightarrow\;\;Gain\;=\;\bf{SP_{(Final)}\;-\;CP}}$

$\\\;\sf{\rightarrow\;\;Gain\;=\;\bf{220\;-\;100}}$

$\\\;\sf{\rightarrow\;\;Gain_{(Final)}\;=\;\bf{\blue{Rs.\;120}}}$

Now using this Gain, we can find the Gain%

$\\\;\boxed{\sf{\pink{Gain\%\;=\;\bf{\dfrac{Gain_{(Final)}}{100}\;\times\;CP}}}}$

By applying values, we get

$\\\;\sf{\Longrightarrow\;\;Gain\%\;=\;\bf{\dfrac{120}{100}\;\times\;100}}$

$\\\;\sf{\Longrightarrow\;\;Gain\%\;=\;\bf{\green{120\;\%}}}$

$\\\;\underline{\boxed{\tt{Hence,\;\:new\;\:gain\:\%\;=\;\bf{\purple{120\;\%}}}}}$

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★ More to know :-

$\\\;\sf{\leadsto\;\;SP\;=\;\dfrac{100\:-\:loss\%}{100}\;\times\;CP}$

$\\\;\sf{\leadsto\;\;CP\;=\;\dfrac{100}{100\;+\;gain\%}\;\times\;SP}$

$\\\;\sf{\leadsto\;\;CP\;=\;\dfrac{100}{100\;-\;loss\%}\;\times\;SP}$

$\\\;\sf{\leadsto\;\;Loss\;=\;CP\;-\;SP}$

$\\\;\sf{\leadsto\;\;Loss\%\;=\;\dfrac{Loss}{100}\;\times\;CP}$