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# A sold an article to B at a profit of 25%, B sold it to C at a loss of 10% and C sold it to D at a profit of 20%. If D pays 27 Rs. Then how much A paid to buy this article?

Last updated date: 13th Jun 2024
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Hint: The problem is of profit and loss. The formula for the profit percent is, Profit percent, $P = \dfrac{{SP - CP}}{{CP}} \times 100$ and for the Loss percent is, $L = \dfrac{{CP - SP}}{{CP}} \times 100$

Complete step by step solution: The problem involves dealing with a case of selling and buying.
If the cost price of A is and selling price is.The profit percent is given by,
${P_A} = \dfrac{{S{P_A} - C{P_A}}}{{C{P_A}}} \times 100$
A sells to B at a profit of 25%, It means Selling Price is 25% more than Cost price
$25 = \dfrac{{S{P_A} - C{P_A}}}{{C{P_A}}} \times 100 \\ S{P_A} = \left( {1 + \dfrac{{25}}{{100}}} \right)C{P_A} \\ S{P_A} = 1.25C{P_A} \cdots (1) \\$
If the cost price of A is $C{P_B}$ and the selling price is$S{P_B}$. The loss percent is given by,
${L_B} = \dfrac{{C{P_B} - S{P_B}}}{{C{P_B}}} \times 100$
B sells to C at a loss of 10%, It means Selling Price is 10% less than Cost price.
$10 = \dfrac{{C{P_B} - S{P_B}}}{{C{P_B}}} \times 100 \\ S{P_B} = \left( {1 - \dfrac{{10}}{{100}}} \right)C{P_B} \\ S{P_B} = 0.9C{P_B} \cdots (2) \\$
Selling price of A is cost price of B . Substitute $S{P_A} = C{P_B}$from equation (1) in equation (2),
$S{P_B} = 0.9\left( {1.25C{P_A}} \right) \\ S{P_B} = 1.125C{P_A} \cdots \left( 3 \right) \\$
If the cost price of A is $C{P_C}$ and the selling price is$S{P_C}$. The profit percent is given by,
${P_C} = \dfrac{{S{P_C} - C{P_C}}}{{C{P_C}}} \times 100$
C sells to D at a profit of 20%, It means Selling Price is 20% more than Cost price.
$20 = \dfrac{{S{P_C} - C{P_C}}}{{C{P_C}}} \times 100 \\ S{P_C} = \left( {1 + \dfrac{{20}}{{100}}} \right)C{P_C} \\ S{P_C} = 1.2C{P_C} \cdots \left( 3 \right) \\$
Selling price of B $S{P_B}$ is the cost price of C $C{P_C}$ . Substitute $S{P_B} = C{P_C}$from equation (3) in equation (4),
$S{P_C} = 1.2\left( {1.125C{P_A}} \right) \\ S{P_C} = 1.35C{P_A} \cdots \left( 5 \right) \\$
Selling price of C is $S{P_C} = 27$ , substitute in equation (5)
$27 = 1.35C{P_A} \\ C{P_A} = \dfrac{{27}}{{1.35}} \\ C{P_A} = 20 \\$
Thus, A bought the article at a cost price of 20 Rs.

Note: The important step is the use percentage in the problems of profit and loss.
It should be clear that the selling price of one person is the cost price of the other person.