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  • Kunal Gaba has n objects, each of weight w. He weighs them in pairs and finds the sum of the weights of all possible pairs is <img alt="120 \mathrm{~g}" src="https://entrancecorner.oncodecogs.

Kunal Gaba has n objects, each of weight w. He weighs them in pairs and finds the sum of the weights of all possible pairs is 120 \mathrm{~g}. When his friend Rakshit weighs them in triplets, the sum of all possible weights is 240 \mathrm{~g}.The value of n is  

Option: 1

7


Option: 2

6


Option: 3

5


Option: 4

10


Answers (1)

best_answer

According to the given condition

\mathrm{\left({ }^n C_2\right)(2 w)=120 \Rightarrow n(n-1) w=120}

And

\mathrm{\left({ }^n C_3\right)(3 w)=240 \Rightarrow n(n-1)(n-2) w=480}

Thus, \mathrm{\quad \frac{n(n-1)(n-2) w}{n(n-1) w}=\frac{480}{120}}

\mathrm{\Rightarrow n-2=4 \quad \Rightarrow \quad n=6}

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