Question

A shopkeeper bought 1600 eggs at 3.75 per dozen he sold 900 of them of them at 2 for 1 rupees and the remaining at 5 for 2 rupees find his profit or loss percent

Answer 1

Answer:

The profit percent is 46%.

Step-by-step explanation:

Given :

A shopkeeper bought 1600 eggs at 3.75 per dozen he sold 900 of them of them at 2 for 1 rupees and the remaining at 5 for 2 rupees.

To Find :

His profit or loss percent.

Solution :

Firstly, finding the cost price of 1600 eggs :

${\implies\sf{C.P \: of \: 12 \: eggs = Rs.3.75}}$

${\implies\sf{C.P \: of \: 1 \: eggs = \dfrac{3.75}{12}}}$

${\implies\sf{C.P \: of \: 1600\: eggs = \dfrac{3.75}{12}}}$

${\implies\sf{C.P \: of \: 1600\: eggs = \dfrac{3.75}{12} \times 1600}}$

${\implies\sf{C.P \: of \: 1600\: eggs = \dfrac{3.75 \times 1600}{12}}}$

${\implies\sf{C.P \: of \: 1600\: eggs = \dfrac{6000}{12}}}$

${\implies\sf{C.P \: of \: 1600\: eggs = \cancel{\dfrac{6000}{12}}}}$

${\implies{\sf{ \underline{\underline{ \red{C.P \: of \: 1600\: eggs = Rs.500}}}}}}$

Hence, the total cost price of 1600 eggs is Rs.500.

$\rule{300}{1.5}$

Now, the shopkeeper sold 900 eggs of them of them at 2 eggs for 1 rupees. So finding the selling price of 900 eggs.

${\implies{\sf{S.P \: of \: 2 \: eggs = Rs.1}}}$

${\implies{\sf{S.P \: of \: 1 \: eggs = \dfrac{1}{2}}}}$

${\implies{\sf{S.P \: of \: 900 \: eggs = \dfrac{1}{2} \times 900}}}$

${\implies{\sf{S.P \: of \: 900 \: eggs = \dfrac{1}{\cancel{2}} \times \cancel{900}}}}$

${\implies{\sf{\underline{\underline{\red{S.P \: of \: 900 \: eggs = Rs.450}}}}}}$

Hence, the selling price of 900 eggs is Rs.450

$\rule{300}{1.5}$

Now, finding the selling price of remaining eggs at 5 egg for 2 rupees.

➜ Remaining egg = 1600 - 900

➜ Remaining egg = 700

${\implies{\sf{S.P \: of \: 5 \: eggs = Rs.2}}}$

${\implies{\sf{S.P \: of \: 1 \: eggs = \dfrac{2}{5}}}}$

${\implies{\sf{S.P \: of \: 700 \: eggs = \dfrac{2}{5}}}}$

${\implies{\sf{S.P \: of \: 700 \: eggs = \dfrac{2}{5} \times 700}}}$

${\implies{\sf{S.P \: of \: 700 \: eggs = \dfrac{2}{\cancel{5}}\times \cancel{700}}}}$

${\implies{\sf{S.P \: of \: 700 \: eggs = 2 \times 140}}}$

${\implies{\sf{\underline{\underline{\red{S.P \: of \: 700 \: eggs = Rs.280}}}}}}$

Hence, selling price of 700 eggs is Rs.280.

$\rule{300}{1.5}$

Calculating the total selling price of 1600 eggs :

S.P = 450 + 280

S.P = Rs.730

Hence, the total selling price of 1600 eggs is Rs.730.

$\rule{300}{1.5}$

Here the cost price of 1600 eggs is Rs.500 and selling price of 1600 eggs is Rs.730. So, here we can see that the shopkeeper made profit.

Calculating the Profit made by shopkeeper :

${\implies{\sf{Profit = S.P - C.P}}}$

${\implies{\sf{Profit = 730 - 500}}}$

${\implies{\sf{\underline{\underline{\red{Profit =Rs.230}}}}}}$

Hence, the profit is Rs.230.

$\rule{300}{1.5}$

Now, finding the profit percent :

$\implies{\sf{Profit \: \% = \dfrac{Profit}{C.P} \times 100}}$

$\implies{\sf{Profit \: \% = \dfrac{230}{500} \times 100}}$

$\implies{\sf{Profit \: \% = \dfrac{230 \times 100}{500}}}$

$\implies{\sf{Profit \: \% = \dfrac{23000}{500}}}$

$\implies{\sf{Profit \: \% = \cancel{\dfrac{23000}{500}}}}$

$\implies{\sf{\underline{\underline{\red{Profit \: \% = 46 \: \%}}}}}$

Hence, the profit percent is 46 %.

$\rule{220pt}{4pt}$

Answer 2

Answer:

The profit percent is 46%

Step-by-step explanation:

In context to the question asked,

We have to find the value of the profit percentage,

It is given that,

The Cost Price for the $12$ eggs = Rs. $3.75$

For calculating, the profit percentage,

The formula to be used:

$Profit Percentage ( \% ) = \frac{Profit}{C.P} \times 100$

He bought a $1600$ eggs at $3.75$ per dozen,

Therefore, C.P. of $1600$ eggs

$=\frac{3.75 \times 1600}{12}$

$=\frac{6000}{12}$

$=Rs.500$

He sold $900$ of them, at $2$ for $1$ Rs.

Now, S.P. of $900$ eggs

$=\frac{1}{2}\times 900$

$= Rs.450$

And the remaining at $5$ for $2$ Rs.

S.P. of remaining $700$ eggs

$=\frac{2}{5}\times 700$

$= Rs.280$

Now, total S.P = $Rs. 450 + Rs. 280$

                        $= Rs. 730$

For calculating the profit,

The formula to be used:

$Profit = S.P - C.P$

           = $730 - 500$

           = $Rs. 230$

Now, substitute all the values in the formula of profit percentage:

$Profit Percentage ( \% ) = \frac{230}{500} \times 100$

                                   = 46%

Hence, the required solution is 46%.