Vinod makes a profit of ₹110 if he sells a certain number of pencils at the price of ₹2.50 per pencil and incurs a loss of ₹55 if he sells the same number of pencils for ₹1.75 per pencil. Find the number of pencils Vinod has.

Question

Accepted Answer

To determine the number of pencils Vinod has, we need to set up equations using the given profit and loss conditions.

**Define Variables**:
   Let n be the number of pencils and let c be the cost price per pencil.

**Set Up Equations Based on Profit Condition**:
   When sold at ₹2.50 per pencil with ₹110 profit:
   
   Total selling price = ₹2.50 × n
   Total cost price = c × n
   Profit = Total selling price - Total cost price = ₹110
   
   This gives us: 2.50n - cn = 110
   Rearranging: cn = 2.50n - 110[2][4]

**Set Up Equations Based on Loss Condition**:
   When sold at ₹1.75 per pencil with ₹55 loss:
   
   Total selling price = ₹1.75 × n
   Total cost price = c × n
   Loss = Total cost price - Total selling price = ₹55
   
   This gives us: cn - 1.75n = 55
   Rearranging: cn = 1.75n + 55[2][4]

**Solve the Equations**:
   Since both expressions equal cn, we can set them equal:
   2.50n - 110 = 1.75n + 55
   
   Simplifying:
   2.50n - 1.75n = 110 + 55
   0.75n = 165
   n = 165 ÷ 0.75 = 220[2][4]

Therefore, Vinod has 220 pencils.

Answer

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