Question

"Shastika bought two watches for Rs 3000. She sold one at a loss of 15% and the other at a gain of 19%, then she found that each watch was sold for the same price. Find the cost price of each watch."

Answer 1

The cost price of the first watch Shastika bought was Rs 1750 and the second watch was Rs 1250. This was determined by solving a system of equations based on the total cost and the percentage gain and loss for each watch, which led to the conclusion that both watches were sold for the same price.

Step-by-step explanation:

To solve the given problem, we need to establish the cost price of both watches and then apply the percentage loss and gain to arrive at the condition given: both watches were sold for the same price.

Let's denote the cost price of the first watch as x and the cost price of the second watch as y. Given that the total cost price is Rs 3000, we can write:

x + y = 3000 ... (1)

According to the problem, the first watch is sold at a 15% loss and the second watch at a 19% gain, and both sell for the same price, so we have:

• 
  
• Price at which the first watch is sold: x - 0.15x = 0.85x
• 
  
• Price at which the second watch is sold: y + 0.19y = 1.19y

Since both watches are sold for the same price, we can equate the selling prices:

0.85x = 1.19y ... (2)

Now we have a system of two equations with two variables:

1. 
   
3. x + y = 3000
4. 
   
6. 0.85x = 1.19y

We can solve this system using substitution or elimination method. Let's use substitution by expressing y in terms of x from equation (1):

y = 3000 - x ... (3)

Substituting y from equation (3) into equation (2), we get:

0.85x = 1.19(3000 - x)

Simplify this equation to find x:

0.85x = 3570 - 1.19x

0.85x + 1.19x = 3570

2.04x = 3570

x = 3570 / 2.04

x = 1750 (Cost price of the first watch)

Substitute the value of x into equation (1) to find y:

y = 3000 - 1750

y = 1250 (Cost price of the second watch)

Therefore, the cost prices of the watches Shastika bought were Rs 1750 and Rs 1250 respectively.