Question

A person purchases 90 pens. Of these, he sold 40 pens at 10% profit and the rest at 20% profit. If he sold all these pens at 15% profit, he gets ₹ 10 less. Find the purchase price of each pen.​

Answer 1

Answer:

Let the Purchase Price of each pen be n.

$\underline{\star\:\sf Situation\:1}$

$\boxed{\bf{\mid{\overline{\underline{\bigstar\:SP\:of\:40\:Pens :}}}}\mid}$

$:\implies\sf SP=CP \times (100+Profit)\%\\\\\\:\implies\sf SP=(No. \times Price) \times (100+10)\%\\\\\\:\implies\sf SP=(40 \times n) \times 110\%\\\\\\:\implies\sf SP=40n \times \dfrac{110}{100}\\\\\\:\implies\sf SP=4n \times 11\\\\\\:\implies\sf SP=44n$

$\rule{80}{1}$

$\boxed{\bf{\mid{\overline{\underline{\bigstar\:SP\:of\:50\:Pens :}}}}\mid}$

$:\implies\sf SP=CP \times (100+Profit)\%\\\\\\:\implies\sf SP=(No. \times Price) \times (100+20)\%\\\\\\:\implies\sf SP=(50 \times n) \times 120\%\\\\\\:\implies\sf SP=50n \times \dfrac{120}{100}\\\\\\:\implies\sf SP=5n \times 12\\\\\\:\implies\sf SP=60n$

$\rule{140}{1}$

$\underline{\star\:\sf Situation\:2}$

$:\implies\sf SP=CP\times (100+Profit)\%\\\\\\:\implies\sf SP=(No. \times Price) \times (100+15)\%\\\\\\:\implies\sf SP=(90 \times n) \times 115\%\\\\\\:\implies\sf SP=90n \times \dfrac{115}{100}\\\\\\:\implies\sf SP=9n \times \dfrac{23}{2}\\\\\\:\implies\sf SP=\dfrac{207n}{2}$

$\rule{200}{2}$

$\underline{\bigstar\:\textbf{According to the Question :}}$

$\dashrightarrow\sf\:\:Situation\:1-Situation\:2=Rs.\:10\\\\\\\dashrightarrow\sf\:\:(44n+60n) -\dfrac{207n}{2}=Rs.\:10\\\\\\\dashrightarrow\sf\:\:104n-\dfrac{207n}{2}=Rs.\:10\\\\\\\dashrightarrow\sf\:\:\dfrac{208n-207n}{2}=Rs.\:10\\\\\\\dashrightarrow\sf\:\:\dfrac{n}{2}=Rs.\:10\\\\\\\dashrightarrow\sf\:\:n=2\times Rs.\:10\\\\\\\dashrightarrow\:\:\underline{\boxed{\sf n=Rs.\:20}}$

⠀

$\therefore\:\underline{\textsf{Purchase Price of each pen is \textbf{Rs. 20}}}.$