Question

A merchant bought a certain number of dolls made of China clay for ₹1200. Yen were damaged during transportation. Then he sold each of the rest for ₹2 more than he had given for it, thereby gaining ₹60 on the whole. Find how many dolls did he buy

Answer 1

Your final answer shall be: 30 dolls

Answer 2

Answer:

Total number of dolls bought = 100

Step-by-step explanation:

Let the total number of dolls bought be x

Total cost price of all the dolls = Rs 1200

$\implies\text{Cost price of one doll = }\frac{1200}{x}$

Number of dolls damaged during the transportation = 10

So, left dolls with the merchant = x - 10

These dolls are sold for a gain of Rs. 60

So, Selling price of (x - 10) dolls = Rs. 1260

$\implies\text{Selling price of one doll = }\frac{1260}{x-10}$

Now, given that the merchant sold each of them for Rs. 2 more

$\implies \frac{160}{x-10}-\frac{1200}{x}=2\\\\\implies x^2-40x-6000=0\\\\\implies x = 100\text{ or }x=-60$

Since, the number of dolls cannot be negative quantity.

Hence, Total number of dolls bought = 100