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**Hint:**Now we know that the man purchases eggs at the rate of 3 eggs for 5 Rs. Hence we can find the cost price of 1 egg. Now let us assume that the man brought x eggs and hence find the cost price of x eggs. Now we are given that the gut sells eggs at a rate of 10 Rs for 5 eggs. Hence we can find the selling price of 1 egg and then the selling price of x eggs. Now we know that profit is nothing but selling price – cost price. Hence we will get an equation in x. we will solve the equation to find the number of eggs brought.

**Complete step by step answer:**

Now a man purchased some eggs at 3 for Rs 5.

This means he paid 5 Rs for each 3 eggs.

This means the cost price of 1 egg is $\dfrac{5}{3}$ .

Let us say the man brought x number of eggs.

Now we have a cost price of 1 egg is $\dfrac{5}{3}$ .

Hence cost price of x eggs will be $\dfrac{5}{3}\times x=\dfrac{5x}{3}......................\left( 1 \right)$

Now we are given that he sold those eggs at 5 for Rs 10.

This means he got 10 Rs for each 5 eggs that he sold.

Hence selling price of 1 egg is $\dfrac{10}{5}=2Rs$

Now Since he had x number of eggs the number of eggs he sold is x.

Hence the selling price of x eggs is 2x …………………. (2)

Now we know that profit is nothing but SP – CP.

Hence from equation (1) and equation (2) we get,

Profit = $2x-\dfrac{5x}{3}$

Now we are given that the profit made is 145Rs. Hence we get,

$145=2x-\dfrac{5x}{3}$

Now multiplying the whole equation by 3 we get

435 = 6x – 5x.

Hence we get x = 435.

**Hence the man purchases 435 eggs.**

**Note:**Now note that the man has made profit and hence the selling price must be greater than cost price. Once we get the number of eggs we can crosscheck the answer and check if the obtained answer also satisfies the given conditions. Also while solving these questions it is better to keep the fractions as it is and not convert them into decimals.

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