Question

Raima sold her gold ring at \[Rs.{\text{ }}26250/ - \]at a profit of \[\;5\% \]. How much did the ring cost her?
A) \[Rs.{\text{ }}26000/ - \]
B) \[Rs.{\text{ }}25000/ - \]
C) \[Rs.{\text{ }}25250/ - \]
D) \[Rs.{\text{ }}24250/ - \]

Answer 1

Hint:Here we will have to apply the concept of Profit & Loss. As a percentage of profit and selling price of gold ring is given, Cost price of gold ring can be obtained from it. We know that Profit is the difference between Selling price & cost price i.e.\[,{\text{ }}Profit{\text{ }} = {\text{ }}S.P{\text{ }}-{\text{ }}C.P\] .So, we can say that Cost price will the sum of Selling price & Profit.

Complete step-by-step answer:
Given, Raima sold her gold ring at \[Rs.{\text{ }}26250/ - \] at a profit of \[\;5\% \].
For finding the cost price we use the formula as.
\[SP{\text{ }} = {\text{ }}CP{\text{ }} + {\text{ }}Profit\]
Here, profit is made on cost price is i.e., $5\% $ on cost price. We use the formula of pofit
i.e.
$Profit = Profit\% \times C.P$
We get,
$\therefore Profit = \dfrac{5}{{100}} \times CP$
Now we put the values of selling price and profit in the formula
We get,
$
\Rightarrow 26250 = CP + \dfrac{5}{{100}} \times CP \\
\\
$
Now, we take CP common in the RHS, We get
$ \Rightarrow CP(1 + \dfrac{5}{{100}}) = 26250$
$ \Rightarrow CP(1 + 0.05) = 26250$
$ \Rightarrow CP \times 1.05 = 26250$
$ \Rightarrow CP = \dfrac{{26250}}{{1.05}} = 25000$
$\therefore $ The Gold ring costs \[Rs.{\text{ }}25000/ - \]to Raima.
So the correct option is (B) \[Rs.{\text{ }}25000/ - \]

Additional information:
Formulas related to this kind of numerical
\[SP{\text{ }} = {\text{ }}CP{\text{ }} + {\text{ }}Profit\left[ {SP = Selling{\text{ }}Price} \right]\]
\[SP{\text{ }} = {\text{ }}CP{\text{ - Loss}}\left[ {cP = \operatorname{Cos} t{\text{ }}Price} \right]\]

Note:
In this type of problem, first it should be observed what is to be determined and what data’s that are provided. The solution can easily be obtained by the basic formulas & form a linear equation with an unknown value to be determined & then solve it. Do the calculations carefully to avoid silly mistakes. Don’t forget to put units (here rupees (Rs.)) because a number without units is meaningless.