MathematicsA store currently charges the same price for each towel that it sells. If the current price of each towel were to be increased by Rupees 1, 10 fewer of the towels could be bought for Rupees 120, excluding sales tax. What is the current price of each towel:

A store currently charges the same price for each towel that it sells. If the current price of each towel were to be increased by Rupees 1, 10 fewer of the towels could be bought for Rupees 120, excluding sales tax. What is the current price of each towel:


  1. A
    1 Rupees
  2. B
    2 Rupees
  3. C
    3 Rupees
  4. D
    4 Rupees

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    Solution:

    Concept- First, start with the number of towels you purchased starting at 120x. Then find out the original price of each towel. Then find a new price for each towel. Then create an equation using the given condition that the price difference for each towel is 1. Solve the formed quadratic equation to find the number of towels you bought for 120. Finally, divide the total cost by the number of towels to get the price of each towel.
    We know that the price of each towel will increase by 1, and now you can buy 10 towels  for 120. Let x be the number of towels you first bought  for 120. The price of the towel can then be calculated by dividing the cost of the towel by the number of towels. So the price of the towel was 120 times Now you can buy 10 less towels and x-10 towels for 120. Therefore, the new price for one towel is Also, the difference between the original price and the new price is .  It is also said that the price will increase by 1 this is,  Take the LCM in the denominator and cross-multiply it to simplify the equation.  Factor the above equation  Find the value of x by equalizing each coefficient to 0 When However, the number of towels cannot be negative, so the number of towels is 40. You need to find the original price of the towel.  Therefore,  substitute the value of x for the original price of the towel. Therefore, the original price of the towel is 3.
    Hence, the correct answer is option (3).
     
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