All the soldiers are arranged in the form of an equilateral triangle i.e., one soldier in the front and 2 soldiers in the second row and 3 soldiers in the third row, 4 soldiers in the fourth row and so on. If 669 more soldiers of another company are added in such a way that all the soldiers now are in the form of a square and each of the sides then contains 8 soldiers less than each side of the equilateral triangle. Initially, how many soldiers were there?

2056

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1540

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1400

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1220

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Solution

The correct option is B 1540
Let the side length of an equilateral triangle be x.
Then, the side length of a square = x - 8
${(x - 8)}^{2} = \frac{x (x + 1)}{2} + 669$
$x^{2} - 33 x - 1210 = 0$
$x = 55$
$N u m b e r o f s o l d i e r s, i n i t i a l l y = \frac{x (x + 1)}{2} = 1540$

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The correct option is B 1540Let the side length of an equilateral triangle be x. Then, the side length of a square = x - 8 (x−8)2 = x(x+1)2 + 669 x2 − 33x − 1210 = 0 x = 55 Number of soldiers, initially = x(x+1)2 = 1540

The correct option is B 1540
Let the side length of an equilateral triangle be x.
Then, the side length of a square = x - 8
${(x - 8)}^{2} = \frac{x (x + 1)}{2} + 669$
$x^{2} - 33 x - 1210 = 0$
$x = 55$
$N u m b e r o f s o l d i e r s, i n i t i a l l y = \frac{x (x + 1)}{2} = 1540$