A piece of cloth costs Rs. 35. If the piece were 4 m longer and each meter were to cost Rs. 1 lesser, then the total cost would remain unchanged. How long is the piece of cloth?

10 m

14 m

12 m

8 m

APEDIA

NTPC Graduate Tier 1

2016 • 02 Apr, 2016 • Shift 2

A piece of cloth costs Rs. 35. If the piece were 4 m longer and each meter were to cost Rs. 1 lesser, then the total cost would remain unchanged. How long is the piece of cloth?

Correct Answer

10 m

Variable Definition: Let the initial length of the cloth be 'x' meters. The initial price per meter becomes (35/x).Condition Formulation: According to the probl......

💡 Analysis & Explanation

Variable Definition ▼

Let the initial length of the cloth be 'x' meters. The initial price per meter becomes (35/x).

Condition Formulation ▼

According to the problem, if length is (x+4) and price per meter is (35/x - 1), the total cost is still 35. So, (x+4) * (35/x - 1) = 35.

Option Testing Method ▼

Instead of solving a quadratic equation, test the options.

Option A Check ▼

If x = 10m, original cost/m = 35/10 = Rs. 3.5. New length = 14m, new cost/m = 3.5 - 1 = 2.5. Total = 14 * 2.5 = 35. This perfectly matches the condition.

Conclusion ▼

The length of the cloth is 10 m.

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A piece of cloth costs Rs. 35. If the piece were 4 m longer and each meter were to cost Rs. 1 lesser, then the total cost would remain unchanged. How long is the piece of cloth?