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

(Q 34B – 30/4/2 – CBSE 2026 Question Paper)

Ans:

Step 1: Let the original length of the cloth be x metres and y is the original price per metre.

From the 1st condition, “total cost is 2,100″

∴ x . y = 2,100

∴ y =

Step 2: From the 2nd condition, “when the length increased by 2 m, the price per metre decreased by 120 for same cost”

∴ ( x + 2).(y – 120) = 2,100

By substituting the value of y, we get:

∴ ( x + 2).( – 120) = 2,100

∴ ( x + 2). = 2,100

∴ ( x + 2).(2100 – 120 x) = 2,100 x

Dividing both sides by 60, we get:

∴ ( x + 2).(35 – 2 x) = 35 x

∴ 35 x – 2 x ² + 70 – 4 x = 35x

∴ – 2 x ² – 4 x + 70 = 0

Dividing both sides by -2, we get:

∴ x ² + 2 x – 35 = 0

Step 3: By mid-term splitting:

∴ x ² + 7 x – 5 x – 35 = 0

∴ x (x + 7) – 5 (x + 7) = 0

∴ (x + 7) (x – 5) = 0

∴ x = – 7 and x = 5.

Step 4: Here, since x is the length of cloth, hence it can not be negative.

∴ we reject x = – 7 and accept x = 5

From equation (i), y = = 420

Therefore, original per metre Rs. 420/m price of cloth and its length is 5 m.

Check: Let’s check validity of our solution at these values of x = 5 and y = 420
Here, x . y = 5 x 420 = 2100 ..1st condition is matched
Next, x + 2 = 5 + 2 = 7 and y – 120 = 420 – 120 = 300.
(x + 2). (y – 120) = 7 x 300 = 2100… 2nd condition is matched.
Since both conditions are matched, our solution is correct.

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