Latest TCS Aptitude Question SOLUTION: Balls are arranged in rows to form an equilateral triangle. The first row consists of one ball, the second row of two balls and so on. If 669 more balls are added, then all the bal

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Balls are arranged in rows to form an equilateral triangle. The first row consists of one ball, the second row of two balls and so on. If 669 more balls are added, then all the balls can be arranged in the shape of a square and each of the sides then contains 8 balls less than each side of the
triangle did. The initial number of balls is

Asked In TCS chaitanya (11 years ago)

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Vignesh  (11 years ago)

1540balls initially there.

n(n + 1)/2 + 669 = (n - 8)^2

=> n^2 - 33n - 1210 = 0
=> (n - 55)(n + 22) = 0
=> n = 55

=> n(n + 1)/2 = (55* 56)/2 = 55 * 28 = 11 * 140 = 1540

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jomon v j  (11 years ago)

Answer 1540

suppose there n rows in equilateral triangle .then no.of balls=n(n+1)/2

now 669 more balls are added and forms a square with sides of n-8 balls.

therefore 669+n(n+1/2=(n-8)²

simplifying we get n²-33n-1210=0

n=55

therefore no.of balls = 55*56/2=1540

actually we are finding a triangular no. which is 669 less than a perfect square.(1540+669=2209,which is a perfect square)

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