Question

Manoj travels from Meerut to Delhi to buy goods which he gets 10 per cent cheaper in Delhi than in Meerut. If his journey expenses are Rs. 160 and he earns Rs. 240 by selling goods at Meerut; calculate his profit per cent.
A.\[2\dfrac{{13}}{{47}}\% \]
B.\[5\dfrac{{15}}{{47}}\% \]
C.\[6\dfrac{{18}}{{47}}\% \]
D.\[9\dfrac{{20}}{{47}}\% \]

Answer 1

Hint: We will first assume the value of the market price of the goods at Delhi and the selling price of the goods at Meerut to be any variable \[x\]. We will calculate the cost price including the expenses of the journey. Then we will equate the difference of the selling price and the cost price with the value of the gain. From there, we will get the value of the variable \[x\] and thus the value of the total cost price. Then we will calculate the value of gain percent using the formula.

Formula used:
We will use the following formulas:
1.\[{\rm{Gain}} = S.P - C.P\], where \[S.P\] is the selling price and \[C.P\] is the cost price.
2.\[{\rm{Gain percentage}} = \dfrac{{{\rm{gain}}}}{{C.P}} \times 100\]

Complete step-by-step answer:
Let the value of the market price of the goods at Delhi and the selling price of the goods at Meerut be \[x\].
Since Manoj buys the goods at 10 percent discount, thus
The cost price of the goods \[ = \dfrac{9}{{100}} \times x = {\rm{Rs}}0.9x\]
The total cost price is equal to the sum of the cost price of the goods and the expenses of the journey.
Therefore, total cost price\[ = {\rm{Rs}}0.9x + {\rm{Rs}}160\] ………….\[\left( 1 \right)\]
Manoj gains Rs. 240 by selling goods at Meerut. So,
\[{\rm{Gain}} = {\rm{Rs}}240\]
We know the formula for calculating gain.
\[{\rm{Gain}} = S.P - C.P\]
Substituting the value of S.P, gain and C.P in the above equation, we get
\[ \Rightarrow 240 = x - 0.9x - 160\]
On simplifying the like terms, we get
\[ \Rightarrow 0.1x = 400\]
On further simplification, we get
\[ \Rightarrow x = {\rm{Rs}}4,000\]
Now, we will put the value of \[x\]in equation \[\left( 1 \right)\].
Total C.P \[ = {\rm{Rs}}0.9 \times 4000 + {\rm{Rs}}160 = {\rm{Rs}}3,760\]
Now, we will calculate the value of gain percent.
Substituting the value of gain and C.P in the formula \[{\rm{Gain\, percentage}} = \dfrac{{{\rm{gain}}}}{{C.P}} \times 100\], we get
\[ \Rightarrow {\rm{Gain\, percentage}} = \dfrac{{240}}{{3760}} \times 100\]
On further simplification, we get
\[ \Rightarrow {\rm{Gain \,percentage}} = 6\dfrac{{18}}{{47}}\% \]
Therefore, the correct answer is option C.

Note: We have calculated the gain percent here. Gain means the extra amount that we earn from selling a product. It is equal to the difference of the selling price and the cost price of the goods. Gain percent is defined as the product of the ratio of the total money gained to the cost price of the goods and 100.