Question

Arjun sells a bicycle to Biju at a profit of 25%. Biju sells it to Charlie at a loss of 20%. If Charlie pays Rs.200 for it, the cost price of the bicycle for Arjun is:
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Answer 1

➤ Given :-

Profit percent of Arjun :- 25%

Loss percent of Biju :- 20%

Cost paid by Charlie :- ₹200

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➤ To Find :-

Coat price of the bicycle for Arjun.

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★ How to do :-

Here, we are given that a bicycle is sold by Arjun to Biju at some profit. The same bicycle is sold by Biju to Charlie. While Biju sold it to Charlie, he lost some percentage. We are also given with that. We are asked to find the cost price of the bicycle when Arjun buys it. So, first we should find the cost price of Biju by using the loss percentage and the cost paid by Charlie to buy the bicycle. Then, we use the cost price of Biju and the profit percent of Arjun and find out the cost price of Arjun. We can see that here the selling price of Biju is as same as the cost paid by Charlie. So, let's solve!!

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➤ Solution :-

We know that the selling price of Biju is same as the cost paid by Charlie. So,

Cost price of Biju :-

${\tt \leadsto \underline{\boxed{\sf \dfrac{100}{(100 - Loss \bf\%)} \times SP}}}$

Substitute the given values.

${\tt \leadsto \dfrac{100}{(100 - 20)} \times 200}$

Write the fraction in lowest form by cancellation method.

${\tt \leadsto \cancel \dfrac{100}{80} \times 200 = \dfrac{5}{4} \times 200}$

Multiply the remaining numbers.

${\tt \leadsto \dfrac{5 \times 200}{4} = \dfrac{1000}{4}}$

Write the obtained fraction in lowest form by cancellation method.

${\tt \leadsto \cancel \dfrac{1000}{4} = 250}$

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We know that the cost price of Biju is same as the selling price of Arjun. So,

Cost price of Arjun :-

${\sf \leadsto \underline{\boxed{\sf \dfrac{100}{(100 + Profit \bf\%)} \times SP}}}$

Substitute the given values.

${\tt \leadsto \dfrac{100}{(100 + 25)} \times 250}$

Write the fraction in lowest form by cancellation method.

${\tt \leadsto \cancel \dfrac{100}{125} \times 250 = \dfrac{4}{5} \times 250}$

Multiply the remaining numbers.

${\tt \leadsto \dfrac{4 \times 250}{4} = \dfrac{1000}{4}}$

Write the obtained fraction in lowest form by cancellation method.

${\tt \leadsto \cancel \dfrac{1000}{4} = 250}$

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${\red{\underline{\boxed{\bf So, \: the \: cost \: price \: of \: Arjun \: is \: \: 250.}}}}$

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$\dashrightarrow$ Some related formulas :-

$\begin{gathered} \small \boxed{\begin{array} {cc} \large \dag \: \sf more \: formulas \\ \\ \sf \bigstar \: Profit = SP - CP \\ \\ \sf \bigstar \: Loss \: = CP - SP \\ \\ \sf \bigstar \: Profit \: percent = \dfrac{profit}{cost \: price} \times 100 \\ \\ \sf \bigstar \: Loss \: percent = \dfrac{loss}{cost \: price} \times 100 \\ \\ \sf \bigstar \: Selling \: price = \dfrac{(100 + profit\%)}{100} \times CP \\ \\ \sf \bigstar \: Selling \: price = \dfrac{(100 - loss\%)}{100} \times CP \end{array}} \end{gathered}$