##### PUSHPAK YADAV

#### profit and loss

#####

**Question**

A person buys 80 apples, price of each apple is Rs. 40. he sells p% apples at a profit of p% and remaining at a profit of (100-p)%. what is the min profit he could have on this deal

18-10-06

**Answer**

A person buys 80 apples, price of each apple is Rs. 40. he sells p% apples at a profit of p% and remaining at a profit of (100-p)%. what is the min profit he could have on this deal

Total Cp of 80 apples =80*40=3200

Profit of P% apples =p% of 80 =4p/5

Cp of 4p/5 =4p/5*40=32p

Profit= (S.P _{1}-C.P _{1})/C.P_{1}*100 =( S.P _{1}-p*40)/(p*40)*100

P%=( S.P _{1}-32p)/(32p)*100

S.P _{1}=(32p^{2}/100)+32p

Similarly Profit of (100-P)% apples

Remaining apples (80-4p/5)

C.P of (80-4p/5) =(80-4p/5)*40= 3200-32p

(100-P)% ={S.P _{2- }(3200-32p) }/{3200-32p }*100

S.P_{2 }=32(100-p)^{2}/100 +32(100-p)

Profit= S.P _{1+} S.P_{2 -} Total Cp of 80 apples

=32(100-p)^{2}/100 +32(100-p)+ (32p^{2}/100)+32p-3200

Differentiate w.r.t P

-64(100-p)/100 -32 +64p/100 +32 =0

-64(100-p)/100 +64p/100=0

{-64(100-p) +64p}/100=0

-64(100-p)+64p=0

-6400+64p+64p=0

128p=6400

P=6400/128= 50 % (Minimum)