Multiple choice general knowledge math & puzzles

A piece of cloth cost Rs 35. if the length of the piece would have been 4m longer and each meter cost Re 1 less , the cost would have remained unchanged. how long is the piece ?

  1. 10

  2. 11

  3. 12

  4. None of the above
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let length = x meters and cost per meter = Rs. y. Given xy = 35 and (x + 4)(y - 1) = 35. Expanding: xy - x + 4y - 4 = 35. Substituting xy = 35: 35 - x + 4y - 4 = 35, so 4y - x = 4. Since y = 35/x, we get 4(35/x) - x = 4, which gives x² + 4x - 140 = 0, so (x + 14)(x - 10) = 0. Therefore x = 10 meters.

AI explanation

Let the length be L meters and the price per meter be p, so L×p = 35. If the length were L+4 meters at (p-1) per meter, cost is unchanged: (L+4)(p-1) = 35. Substituting p = 35/L into the second equation and simplifying gives L² + 4L - 140 = 0, which factors/solves via the quadratic formula to L = 10 (the other root is negative and rejected). Checking: at L=10, p=3.5/m, cost=35; at L=14, p=2.5/m, cost=35 -- both match, confirming the piece is 10 meters long.

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