Question

A shopkeeper buys 100 pens for 200 rupees and sells 20 of them at the gain of 10% at what gain percent must he sell the remainder so as to gain 20% in all

Answer 1

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

${\boxed{\sf\:{Cost\;Price\;of\;100\;pens :-}}}$

= 200

${\boxed{\sf\:{Cost\;Price\;of\;one\;pen :-}}}$

$\tt{\rightarrow\dfrac{200}{100}}$

${\boxed{\sf\:{Cost\;Price\;of\;20\;pens :-}}}$

$\tt{\rightarrow\dfrac{200}{100}\times 20}$

= Rs.40

$\text{Gain\;percent\;of\;20\;pens}$

= 10%

${\boxed{\sf\:{Selling\;Price\;of\;20\;pens :-}}}$

$\tt{\rightarrow 10+\dfrac{Gain}{100}\times Cost\;Price}$

$\tt{\rightarrow 100+\dfrac{10}{100}\times 40}$

= 44

Gain percent of whole lot 100 pens

= 20%

${\boxed{\sf\:{Selling\;Price\;of\;100\;pens :-}}}$

$\tt{\rightarrow 100+\dfrac{20}{100}\times 200}$

= 240

${\boxed{\sf\:{Cost\;Price\;of\;80\;pens :-}}}$

= 200 - 40

= 160

${\boxed{\sf\:{Selling\;Price\;of\;80\;pens :-}}}$

= 240 - 44

= 196

${\boxed{\sf\:{Gain\;of\;80\;pens :-}}}$

= 196 - 160

= 36

$\tt{\rightarrow Gain=\dfrac{36}{160}\times 100}$

= 22.5%

Answer 2

AnswEr :

჻ He will Sell at 22.5% Gain.

Solution :

▣ CP of 100 Pens = Rs. 200

» CP of 1 Pen = $\large\tt{\frac{Rs.200}{100}}$

» CP of 1 Pen = Rs. 2

» CP of 20 Pen = 2 × 20

» CP of 20 Pen = Rs. 40

▣ Gain% = 10% [ Given ]

▣ SP = CP × G%

» SP = 40 × $\large\tt{\frac{(100+10)}{100}}$

» SP = 40 × $\large\tt{\frac{110}{100}}$

» SP = 4 × 11

» SP of 20 Pens = Rs. 44

━━━━━━━━━━━━━━━━━━━━━━━━

▣ Gain% on 100 pens = 20%

▣ SP = CP × G%

» SP = 100 × $\large\tt{\frac{(100+20)}{100}}$

» SP = 200 × $\large\tt{\frac{120}{100}}$

» SP = 2 × 120

» SP of 100 Pens = Rs. 240

━━━━━━━━━━━━━━━━━━━━━━━━

☢ CP of 80 Pens = CP of 100 Pens - CP of 20 Pens

➟ CP of 80 Pens = Rs. (200 - 40)

➟ CP of 80 Pens = Rs. 160

☢ SP of 80 Pens = SP of 100 Pens - SP of 20 Pens

➟ SP of 80 Pens = Rs. (240 - 44)

➟ SP of 80 Pens = Rs. 196

━━━━━━━━━━━━━━━━━━━━━━━━

➟ Gain = SP - CP

➟ Gain = Rs. (196 - 160)

➟ Gain = Rs. 36

_______________________________

$\boxed {\bold{gain\% = \frac{gain}{CP} \times 100}}$

➟ Gain% = $\large\tt{\frac{36}{160}}$ × 100

➟ Gain% = 22.5%