Question

A dealer purchased 100 football for to 80 each. He sells 20 of them at a gain of 5% .At what gain% must be sell the remaining footballs so as to gain 20% on the whole

Answer 1

Solutions :-


Given :
A dealer purchased 100 football for Rs 80 each
So, The cost price of 100 football = 80 × 100 = Rs 8000



Now,
Find the Selling price of 20 football at a gain of 5% :-

Cost Price of 20 football = Rs 20 × 80 = Rs 1600

S.P = C.P + Profit % of C.P
= 1600 + 5% of 1600
= 1600 + 0.05 × 1600
= 1600 + 80 = 1680

So, selling price of 20 football = Rs 1680


Now,
Find the Selling price of total football to gain 20 % :-

S.P = C.P + Profit % of C.P
= 8000 + 20% of 8000
= 8000 + 0.2 × 8000
= 8000 + 1600
= 9600

So, selling price of 100 football is Rs 9600



We have,
Remaining football = 100 - 20 = 80
Cost Price of 80 football = Rs 80 × 80 = Rs 6400
Selling price of remaining football = Rs (9600 - 1680) = Rs 7920


Profit on remaining football = S.P - C.P
= Rs (7920 - 6400)
= Rs 1520

Profit % = (profit × 100)/C.P %
= (1520 × 100)/6400 %
= 152000/6400 %
= 23.75 %



Hence,
The remaining football sold at the gain of 23.75%

Answer 2

Here is your solution

Given :-

A dealer purchased 100 football for to Rs 80 each.

so cost of 100 football =100 ×80 = Rs8000

Now

we have to find selling price 20 football at gain 5%.

cost of 20 football = 20 × 80 = Rs 1600.

we know that

Sp = CP +profit % of c.p

sp= 1600+ 80

sp=1680

Sp of 20 football  is Rs 1680.

Now

we have to find selling price of total football.

Sp = CP +profit % of c.p

sp=8000+1600(20%of 8000)

sp= 9600

Sp of 100 football  is Rs 9600.

Now number of remaining football =?

=100-20

=80 football.

cost of 80 football =80×80 = Rs 6400.

Selling price of remaining football =>9600-1680= Rs 7920.

profit of remaining football =?

profit= sp-cp =>7920-6400= Rs 1520.

Profit percentage = profit ×100/cp%

=>1520×100/6400

=>23.75%

Hence

remaining footballs sold at gain % = 23.75%

Hope it helps you