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The total cost of a washing machine with a toaster was Rs 10500. The toaster was sold at a profit of 22% and the washing machine at a loss of 12%. If the sale price was the same in both the items, then the cost price of the cheaper item was ______.a.RS 3250 b.Rs 4100 c.RS 4400d.RS 7100

Question

The total cost of a washing machine with a toaster was Rs 10500. The toaster was sold at a profit of 22% and the washing machine at a loss of 12%. If the sale price was the same in both the items, then the cost price of the cheaper item was ______.a.RS 3250 b.Rs 4100 c.RS 4400d.RS 7100

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Solution

Let's denote:

  • The cost price of the toaster as 'T'
  • The cost price of the washing machine as 'W'

From the problem, we know that:

  1. T + W = 10500 (The total cost of both items is Rs 10500)
  2. T * 1.22 = W * 0.88 (The toaster was sold at a 22% profit and the washing machine at a 12% loss, but their selling prices were the same)

We can solve these equations step by step:

Step 1: Express T from the first equation: T = 10500 - W Step 2: Substitute T in the second equation: (10500 - W) * 1.22 = W * 0.88 Step 3: Solve the equation for W: 12810 - 1.22W = 0.88W Step 4: Combine like terms: 2.1W = 12810 Step 5: Solve for W: W = 12810 / 2.1 = 6100

Substitute W = 6100 in the first equation to find T: T = 10500 - 6100 = 4400

So, the cost price of the cheaper item was Rs 4400. Therefore, the answer is c. RS 4400.

This problem has been solved

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