Question

Rakesh bought some chocolates at 10 for Rs.1.50 and equal number at 20 paisa each. He sold them at the rate of 20 for Rs.4 and made a profit of Rs.10. How many chocolates did he purchase?
A. $100$
B. $200$
C. $300$
D. $400$

Answer 1

According to the question we have to determine the number of chocolates he purchased when Rakesh bought some chocolates at 10 for Rs.1.50 and equal number at 20 paisa each. He sold them at the rate of 20 for Rs.4 and made a profit of Rs.10. So, first of all we have to count the number of chocolates purchased by Rakesh.
Now, we have to determine the price of the one chocolate which will be the cost price of the one chocolate.
Now, we have to determine the cost price of twice the number of chocolate.
Now, as mentioned in the question, he sold 20 chocolates at the rate of Rs.4, so now we have to determine the selling price of the one chocolate, same as we determine the cost price of the one chocolate.
As mentioned in the question that profit earned by the Rakesh is Rs.10 hence, with the help of profit and obtained selling and cost price we can determine the total number of chocolates purchased by him for which we have to subtract the selling price to the cost price.

Complete step-by-step answer:
Step 1: First of all we have to let the number of chocolates purchased by the Rakesh as mentioned in the solution hint. Hence,
$\Rightarrow$Let the number of chocolates$= x$
Step 2: Now, we have to determine the price of the one chocolate which will be the cost price of the one chocolate as we know that 10 chocolates are parched at the rate of Rs.1.50. Hence,
$\Rightarrow$Cost price of the one chocolate$= \dfrac{{1050}}{{10}}$
$\Rightarrow$Cost price of the x chocolates$= 0.15x$
Step 3: Now, we have to determine the cost price of the another 2x chocolates which can be determined as,
$\Rightarrow$Cost price of the 2x chocolates$= 0.15x + 0.2x$
$= Rs0.35x$
Step 4: Now, as mentioned in the question, he sold the 20 chocolates at the rate of Rs.4, so now we have to determine the selling price of the one chocolate, same as we determine the cost price of the one chocolate. Hence,
$\Rightarrow$Selling price of 1 chocolate$\to \dfrac{4}{{20}} = Rs0.20$
Step 5: Now, we have to determine the selling price of 2x chocolates which can be determine as,
$\Rightarrow$Selling price of 2x chocolates$= 2 \times 0.20x$
$= 0.40x$
Step 6: Now, as mentioned in the question that profit earned by the Rakesh is Rs.10 hence, with the help of profit and obtained selling and cost price we can determine the total number of chocolates purchased by him for which we have to subtract the selling price to the cost price. Hence,
Profit on the 2x chocolates:
$= (0.4x - 0.35x) \\\ = 0.05x \\\$
Hence,
$\Rightarrow 0.05x = 10 \\\ \Rightarrow x = \dfrac{{1000}}{5} \\\ \Rightarrow x = 200 \\\$

Final solution: Hence, we have determined the total number of chocolates purchased by Rakesh which are 200 in number. Therefore option (B) is correct.

Note:
It is necessary that we have to determine the cost of 1 chocolate which can be determined by the cost price of all the 10 chocolates and the number of chocolates we let in.
To determine the profit it is necessary that we have to subtract the cost price from the selling price and then as mentioned in the question that profit is of Rs.10 hence we can obtain the required value of x.