Question

rohan sells a T.V to Roshan for 8800 making a profit of 10% .Roshan sells the T.V to sushant making a profit of 10%. find the amount paid by Rohan and roshan respectively to buy the T.V find the purchase price of sushant​

Answer 1

➤ Answer :-

$\tt Given \begin{cases} \tt Selling \: price (Rohan \: to \: Roshan):- \: 8800 \\ \tt Profit (Roshan \: to \: Sushant):- \: 10 \bf\% \end{cases}$

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$\tt To \: Find \begin{cases} \tt Amount \: paid \: by \: while \: purchasing \\ \tt Purchase \: price \: of \: Sushant \end{cases}$

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★ How to do :-

Here, we are given that Rohan sells a television to Roshan by 10% of profit. The same television is sold by Roshan to Rohan for 10% of profit. We should find the amount paid by Rohan while buying the television and then the selling price of Roshan i.e, the purchase price of Sushant. So, first we should find the cost price of Rohan by using the formula given below and the the amount paid by Sushant to Roshan. So, let's solve!!

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➤ Solution :-

Cost price of Rohan :-

${\tt \leadsto \dfrac{100}{(100 + 10)} \times 8800}$

${\tt \leadsto \dfrac{100}{\cancel{110}} \times \cancel{8800} = \dfrac{100}{1} \times 80}$

${\tt \leadsto \dfrac{100 \times 80}{1} = \dfrac{8000}{1}}$

${\tt \leadsto \cancel \dfrac{8000}{1} = \boxed{\tt Rs \: \: 8000}}$

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Purchase price of Sushant :-

${\tt \leadsto \dfrac{(100 + 10)}{100} \times 8800}$

${\tt \leadsto \dfrac{110}{\cancel{100}} \times \cancel{8800} = \dfrac{110}{1} \times 8}$

${\tt \leadsto \dfrac{110 \times 8}{1} = \dfrac{880}{1}}$

${\tt \leadsto \cancel \dfrac{880}{1} = \boxed{\tt Rs \: \: 880}}$

$\Huge\therefore$ The cost price of Rohan is ₹8000 and the purchase price of Sushant is ₹880.

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$\dashrightarrow$ Some related formulas :-

$\small\boxed{ \begin{array}{cc}\large\sf\dag \: {\underline{More \: Formulae}} \\ \\ \bigstar \: \sf{Gain = S.P – C.P} \\ \\ \bigstar \:\sf{Loss = C.P – S.P} \\ \\ \bigstar \: \sf{Gain \: \% = \Bigg( \dfrac{Gain}{C.P} \times 100 \Bigg)\%} \\ \\ \bigstar \: \sf{loss \: \% = \Bigg( \dfrac{loss}{C.P} \times 100 \Bigg)\%} \\ \\ \bigstar \: \sf{S.P = \dfrac{100+Gain\%}{100} \times C.P} \\ \\ \bigstar \: \sf{ C.P =\dfrac{100}{100+Gain\%} \times S.P} \\ \\\bigstar \: \sf{ S.P = \dfrac{100-loss\%}{100} \times C.P} \\ \\ \bigstar \: \sf{ C.P =\dfrac{100}{100-loss\%} \times S.P}\end{array}}$