Question

The total cost of certain piece of cloth was ₹ 2,100. During special sale time, the shopkeeper offered 2 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?

Answer 1

Let original length be L metres and original price be P per metre.

L × P = 2100 ⇒ `P = 2100/L`

New length = L + 2

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

Given: P_new = P_old – 120.

`2100/L - 2100/(L + 2) = 120`

`17.5/L - 17.5/(L + 2) = 1`

`17.5 ((L + 2 - L)/(L(L + 2))) = 1`

`35/(L^2 + 2L) = 1` ⇒ L² + 2L – 35 = 0

Factorizing: (L + 7)(L – 5) = 0.

Since length cannot be negative, L = 5 m.

Original price P = `2100/5` = 420.

Original price was 420 per metre and length was 5 m.