Question

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

Answer 1

Hey!!!!! __________________


→CP of 100 pens= Rs200


→Gain= 20%


→SP=
$\frac{100 + gain\%}{100} \times cp$




$= \frac{100 + 20}{100} \times 200 \\ = 120 \times 2 \\ = 240$



→CP of 20 pens= 200/100*20
= 40



→Gain%= 10%
→SP of 20 pens=



$= \frac{100 + 10}{100} \times 40 \\ = \frac{110}{100} \times 40 \\ = 44$





→Remaining CP= 200-40
= 160




→Remaining SP= 240-44
= 196




→Gain= SP-CP
= 196-160
= 36




$gain\% = \frac{gain}{cp} \times 100$

$= \frac{36}{160} \times 100 \\ = 22.5\%$
Thank You!!! ____________

Hope this will be helpful for you!

Answer 2

Answer:   Gain percent must be 22.5% on selling the remainder pens so as to gain 20% in all.

Step-by-step explanation:

∵ CP of 100 pens= Rs200

Gain= 20%

SP =  $\frac{100+gain percentage}{100} \m$×$C.P.$

     =$\frac{100+20}{100}$×$200$

     =120×2

     =240

SP of 100 pens is Rs240.

Now according to question, a shopkeeper sells 20 of them at a gain of 10%

First we will find ,

CP of 20 pens= 200/100 x 20

                        = 40

Gain% = 10%

Now, SP of 20 pens=$\frac{100+gainpercentage}{100}$×$C.P.$

SP of 20 pens=$\frac{100+10}{100}$×$40$

                          =$\frac{110}{100}$×$40$

=44

∵Remaining CP= 200-40

= 160

Similarly,

Remaining SP= 240-44

= 196

∴Gain= SP-CP

       = 196-160

         = 36

Hence, $gain$% =$\frac{gain}{C.P.}$×$100$

=$\frac{36}{160}$×$100$

=22.5%

Hence, gain percent must be 22.5% on selling the remainder pens so as to gain 20% in all.

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