Question

By selling a watch for \[{\rm{Rs1275}}\], Javed lost \[15\% \]. At what price should he sell to make a profit of \[10\% \]?

Answer 1

Hint:
Here, we will assume the cost price of the object to be some variable. Then using the formula of loss and given information we will find two values of loss. Equating both the values and solving them further will give us the cost price. We will then find the profit using the obtained cost price and given information. Then we will add profit to the cost price to get the required selling price.

Formula Used:
We will use the following formulas:
\[{\rm{Loss}} = {\rm{CP}} - {\rm{SP}}\]
\[{\rm{Profit}} = {\rm{SP}} - {\rm{CP}}\]

Complete Step by step Solution:
Let the cost price (C.P.) of the watch be \[x\].
The given selling price of the watch is \[{\rm{Rs1275}}\]
Substituting the values of cost price and selling price in the above formula \[{\rm{Loss}} = {\rm{CP}} - {\rm{SP}}\] , we get
\[ \Rightarrow {\rm{Loss}} = x - 1275\] ……………………………….\[\left( 1 \right)\]
But, it is given that Javed lost \[15\% \].
Since, the C.P. is \[x\]
Therefore, the loss of Javed is \[15\% \] of \[x\]
\[ \Rightarrow {\rm{Loss}} = \dfrac{{15}}{{100}}x\] ………………………………….\[\left( 2 \right)\]
Now equating equation \[\left( 1 \right)\] and \[\left( 2 \right)\], we get,
\[\dfrac{{15}}{{100}}x = x - 1275\]
\[ \Rightarrow x - \dfrac{{15x}}{{100}} = 1275\]
Taking LCM on the LHS, we get
\[ \Rightarrow \dfrac{{100 - 15x}}{{100}} = 1275\]
Multiplying both sides by 100, we get
\[ \Rightarrow 85x = 127500\]
Dividing both sides by 85, we get
\[ \Rightarrow x = 1500\]
Therefore, the cost price (C.P.) of the watch is \[{\rm{Rs}}1500\]
Now, we have to find that at what price he should sell the watch to make a profit of \[10\% \]
Here, Cost price (C.P.) of the watch is \[{\rm{Rs}}1500\]
Profit is \[10\% \] of C.P.
Hence, \[{\rm{Profit}} = \dfrac{{10}}{{100}} \times 1500 = {\rm{Rs}}150\]
Hence, substituting the values of cost price and profit in the formula \[{\rm{Profit}} = {\rm{SP}} - {\rm{CP}}\], we get,
\[150 = {\rm{SP}} - 1500\]
Adding 1500 on both sides, we get
\[ \Rightarrow {\rm{SP}} = 1650\]

Therefore, Javed should sell the watch at \[{\rm{Rs}}1650\] in order to make a profit of \[10\% \].

Note:
Cost Price is the price at which an object is purchased, whereas Selling Price is the price at which an article is sold to a customer. Whenever our cost price is greater than our selling price, it means that we are selling a particular item at a lesser price than we had paid to buy it; hence, it’s a loss. Similarly, whenever our cost price is lesser than our selling price, it means that we are making extra money or profit.