Question

What is the ratio by which the C.P has to be multiplied to get S.P, if profit is 10%?

Answer 1

Hint: This is a formula-based question. The formula by which C.P, S.P, % profit are related is $\% profit = \dfrac{{S.P - C.P}}{{C.P}} \times 100$.
Where S.P= selling price, C.P=cost price and %profit=the profit in percentage.
If the S.P and C.P is known then the %profit can be found out using the above relation.

Complete step-by-step solution:
Given,
%profit=10
C.P=?
S.P=?
In order to find the ratio by which C.P has to be multiplied to get S.P we have to use the formula
$\% profit = \dfrac{{S.P - C.P}}{{C.P}} \times 100$
On substituting the values of the given variables
$10 = \dfrac{{S.P - C.P}}{{C.P}} \times 100$
Dividing both sides by 100
$\dfrac{{10}}{{100}} = \dfrac{{S.P - CP}}{{C.P}}$
On simplifying further,
$\dfrac{1}{{10}} = \dfrac{{S.P - C.P}}{{C.P}}$
Multiplying both sides by C.P
$ \Rightarrow $$\dfrac{{C.P}}{{10}} = S.P - C.P$
Adding C.P both sides,
$\dfrac{{C.P}}{{10}} + C.P = S.P$
Or,
$S.P = \dfrac{{C.P}}{{10}} + C.P$
$ \Rightarrow $$S.P = \dfrac{{C.P + 10C.P}}{{10}}$
$ \Rightarrow S.P = \dfrac{{11C.P}}{{10}}$
$ \Rightarrow S.P = \left( {\dfrac{{11}}{{10}}} \right)C.P$
$\therefore $The fraction by which the C.P is multiplied to get S.P is $\dfrac{{11}}{{10}}$
So the final fraction is $\dfrac{{11}}{{10}}$ .

Note: As this type of question formula is being used therefore the formula is to be remembered in order to solve the question. Substitute the values of the variable in the equation carefully otherwise the required answer would not come. Do not make any calculation mistake to avoid getting any wrong answer. Always try to solve the question step by step. In this question the fraction comes already but if the values are in decimal then after solving, change the final answer from decimal to fraction. If the values substituted are not right then the final answer would not come. If the values of any two variables are known then the value of the unknown variable can be found.