Math, asked by Sony2928, 8 months ago

Mukesh sells two shirts. The cost price of the first shirt is equal to the selling price of the second shirt. The first shirt is sold at a profit of 30% and the second shirt is sold at a loss of 30%. What is the ratio of the selling price of the first shirt to the cost price of the second shirt?

A) 91 : 100 B) 100 : 91 C) 31 : 50 D) 50 : 31

Answers

Answered by TheVenomGirl
3

Answer :-

  • A) 91 : 100

Explanation :-

 \sf \: First \:  shirt  \: is  \: sold \:  at \:  a  \: profit  \: of  \: 30\% =  \dfrac{3}{10}

  • Let CP of the first shirt be 10 and profit be 3.

So,

 { \red{\sf {\: SP  \: of  \: the  \: first  \: shirt :  - }}}  \\ \sf \: = 10 + 3  \\\sf\:=13\frac{(CP)1}{(SP)1} \\ \sf \: = \frac{10}{13}----(1)

Similarly,

 \sf \: Second  \: shirt \:  is \:  sold \:  at \:  a \:  loss \:  of  \: 30 \% =  \dfrac{3}{10}

  • Let CP of the second shirt be 10 and loss be 3.

So,

 { \red{\sf {\: SP \:  of \:  the \:  second \:  shirt \:  be : - }}} \\  \sf \: = 10 - 3  \\ \sf \:  =  \frac{7(CP)2}{(SP)2 } \\ \sf \:   =  \frac{10}{7}       ----(2)

  • CP of the first shirt is equal to the SP of the second shirt. {Given}

Multiplying 7 to eqn (1) and 10 to eqn (2) we get,

 \implies \sf \frac{(CP)1}{(SP)1}  =  \frac{70}{91} \\ \implies\sf \frac{(CP)2}{(SP)2}  =  \frac{100}{70}

Ratio of the selling price of the first shirt to the cost price of the second shirt is 91 : 100

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