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Question

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A) \[Rs.{\text{ }}26000/ - \]

B) \[Rs.{\text{ }}25000/ - \]

C) \[Rs.{\text{ }}25250/ - \]

D) \[Rs.{\text{ }}24250/ - \]

Answer

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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) \[Rs.{\text{ }}25000/ - \]

Formulas related to this kind of numerical

\[SP{\text{ }} = {\text{ }}CP{\text{ }} + {\text{ }}Profit\left[ {SP = Selling{\text{ }}Price} \right]\]

\[SP{\text{ }} = {\text{ }}CP{\text{ - Loss}}\left[ {cP = \operatorname{Cos} t{\text{ }}Price} \right]\]

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.