Question

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

Answer 1

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