Area of a rectangle having its length and breadth expressed as integers gets increased by 103% when its sides are increased by x% (say of length) and y% (say of breadth), where x and y are two distinct integers, greater than 0 but less than 100.

Then find the values of x and y if the measurements (of length and breadth) are integers prior to and post increment operation. Also find the numerical values of the measurements in all possible cases prior and post increment.


closed as off-topic by boboquack, Rand al'Thor, Glorfindel, Gamow, Sconibulus Jul 19 '17 at 16:42

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We need to find x and y such that $(100 + x) * (100 + y) = 20300$, so let's look at a prime factorisation of $20300$:

$20300 = 2^2 * 5^2 * 7 * 29$

So we need to make two numbers from these factors, greater than $100$ but less than $200$. We can try $29 * 5 = 145$, which pairs with $2^2 * 5 * 7 = 140$, so $x = 40$ and $y = 45$ (or vice versa). Alternately, $116 * 175$ gives $x = 16$, $y = 75$.

  • $\begingroup$ Yes, @Curtis J. Reubens, you got it correct ! $\endgroup$ – Mea Culpa Nay Jul 18 '17 at 13:52

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