Question

The total cost of certain piece of cloth was ₹ 2,100. During special sale time, the shopkeeper offered \(2 \text{ m}\) extra cloth for free thus reducing the price of cloth per metre by ₹ 120. What was the original per metre price of cloth and its length?

Hint:

In cost-quantity problems, the equation \(\text{Rate}_1 - \text{Rate}_2 = \text{Difference}\) is a standard template that leads to a quadratic equation in quantity.

Answer 1

Step 1: Understanding the Situation:
Total cost of cloth = ₹2100 (fixed).
When length increases by 2 m, price per metre decreases by ₹120.

Step 2: Let Original Length and Price be:
Let original length = L metres
Let original price per metre = P

So,
L × P = 2100
P = 2100 / L

New length = L + 2
New price per metre = 2100 / (L + 2)

Given decrease in price is ₹120:
Original price − New price = 120

2100/L − 2100/(L + 2) = 120

Step 3: Solving the Equation:
Take LCM:
2100[(L + 2 − L) / L(L + 2)] = 120
2100(2) / [L(L + 2)] = 120
4200 / [L² + 2L] = 120

Divide both sides by 120:
35 / (L² + 2L) = 1

So,
L² + 2L = 35
L² + 2L − 35 = 0

Factorising:
(L + 7)(L − 5) = 0

L = −7 (not possible)
L = 5

Step 4: Finding Original Price:
P = 2100 / 5
P = ₹420 per metre

Final Answer:
Original length = 5 metres
Original price = ₹420 per metre