If some balls are arranged in the form of an equilateral triangle with n rows such that $r^{t h}$ row of balls has $r$ balls in it. if $99$ more balls are added to existing one and the balls can now form a square with $(n - 2)$ balls in each row. Then the number of balls that formed the equilateral triangle.

190

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290

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100

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140

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Solution

The correct option is D $190$
$\frac{n (n + 1)}{2} + 99 = (n - 2)^{2} \Rightarrow n^{2} - 9 n - 190 = 0 \Rightarrow n = 19 \Rightarrow$ number of balls $= \frac{19.20}{2} = 190$

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If some balls are arranged in the form of an equilateral triangle with n rows such that rth row of balls has r balls in it. if 99 more balls are added to existing one and the balls can now form a square with (n−2) balls in each row. Then the number of balls that formed the equilateral triangle.

The correct option is D 190n(n+1)2+99=(n−2)2⇒n2−9n−190=0⇒n=19⇒ number of balls =19.202=190

The correct option is D $190$
$\frac{n (n + 1)}{2} + 99 = (n - 2)^{2} \Rightarrow n^{2} - 9 n - 190 = 0 \Rightarrow n = 19 \Rightarrow$ number of balls $= \frac{19.20}{2} = 190$