Question

Harish bought a cycle for rupees 1600 and sold it to Mayank at a profit of 12 1/2%. Mayank sold the same to Rajiv at a profit of 10%. For how much did Rajiv get it?​

Answer 1

➤ Given :-

• Cost price (Harish) :- ₹1600
• Profit percent (Harish) :- 12½%
• Profit percent (Mayank) :- 10%

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➤ To Find :-

Selling price of Mayank to Rajiv.

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➤ Formula required :-

${\large \dashrightarrow \orange{\boxed{\tt \gray{\dfrac{(100 + Profit \bf\%)}{100} \times CP}}}}$

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★ How to do :-

Here, we are given with the cost price of a bicycle bought by Harish. He had sold it to Mayank at a profit of 12½%. Next, the Mayank had sold it to Rajiv at a profit of 10%. We are asked to find the amount that Rajiv pays to Mayank while receiving the bicycle. So, first we should find the selling price of Harish to Mayank i.e, the cost price of Mayank. Then, we can find the amo that Rajiv gives to Mayank by using the given formula. So, let's solve!!

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➤ Solution :-

Selling price of Harish :-

${\tt \leadsto \dfrac{(100 + 12.5)}{100} \times 1600}$

${\tt \leadsto \dfrac{112.5}{100} \times 1600 = \dfrac{1125}{1000} \times 1600}$

${\tt \dfrac{1125}{\cancel{1000}} \times \cancel{1600} = \dfrac{1125}{5} \times 8}$

${\tt \leadsto \dfrac{1125 \times 8}{5} = \dfrac{9000}{5}}$

${\tt \leadsto \cancel \dfrac{9000}{5} = 1800}$

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Now,

Selling price of Mayank to Rajiv :-

${\tt \leadsto \dfrac{(100 + 10)}{100} \times 1800}$

${\tt \leadsto \cancel \dfrac{110}{100} \times 1800 = \dfrac{11}{10} \times 1800}$

${\tt \leadsto \dfrac{11}{\cancel{10}} \times \cancel{1800} = \dfrac{11}{1} \times 180}$

${\tt \leadsto \dfrac{11 \times 180}{1} = \dfrac{1980}{1}}$

${\tt \leadsto \cancel \dfrac{1980}{1} = \boxed{\tt Rs \: \: 1980}}$

$\Huge\therefore$ Rajiv got that bicycle for ₹1980.

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$\dashrightarrow$ Some related formulas :-

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