If the cost price of 25 books is equal to the selling price of 20 books, then find the gain/loss percentage?
Answers
Answer:
The gain percent is 25%.
Solution:
Let C.P. of a book = Rs. X
So, C.P. of 25 books = Rs. 25 X
And,
S.P. of a book = Rs. Y
So, S.P. of 20 books = Rs. 20 Y
Given that
25X = 20Y
\frac{X}{Y}=\frac{25}{20}=\frac{4}{5} \ldots \ldots \ldots \ldots(1)
Y
X
=
20
25
=
5
4
…………(1)
We know that,
\ Profit \%=\left(\frac{profit}{c.P}\right) \times 100 Profit%=(
c.P
profit
)×100
=\left\{\frac{S . P-C . P}{C . P}\right\} \times 100={
C.P
S.P−C.P
}×100
\ Profit \%=\left\{\frac{S . P-C . P}{C . P}\right\} \times 100 Profit%={
C.P
S.P−C.P
}×100
\ Profit \%=\left\{\frac{Y-X}{X}\right\} \times 100 Profit%={
X
Y−X
}×100
\ Profit \%=\left(\frac{Y}{x}-1\right) \times 100 Profit%=(
x
Y
−1)×100
[Since\frac{x}{Y}=\frac{4}{5}
Y
x
=
5
4
\ Profit \%=\left(\frac{5}{4}-1\right) \times 100 Profit%=(
4
5
−1)×100
\ Profit \%=\left(\frac{5-4}{4}\right) \times 100 Profit%=(
4
5−4
)×100
\ Profit \%=\frac{1}{4} \times 100 Profit%=
4
1
×100
\ Profit \%=25 \% Profit%=25%
By selling the books as per the cost price and selling price given in the question, the gain is 25 percentage.