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 $$120g$$. When his friend Rakshit weighs them in triplets, the sum of all possible weights is $$240g$$. The value of n is

Question

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 $$120g$$. When his friend Rakshit weighs them in triplets, the sum of all possible weights is $$240g$$. The value of n is

Infinity Learn · Accepted Answer

According to the given conditionand           $$nC2(2w)=120$$ ⇒ $$n(n$$−$$1)w=120$$ $$nC3(3w)=240$$ ⇒ $$n(n$$−$$1)(n$$−$$2)w=480Thus$$,      $$n(n$$−$$1)(n$$−$$2)wn(n$$−$$1)w=480120$$⇒ n−$$2=4$$ ⇒ $$n=6$$

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 120g. When his friend Rakshit weighs them in triplets, the sum of all possible weights is 240g. The value of $n$ is

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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 120g. When his friend Rakshit weighs them in triplets, the sum of all possible weights is 240g. The value of n is

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Ready to Test Your Skills?

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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 120g. When his friend Rakshit weighs them in triplets, the sum of all possible weights is 240g. The value of $n$ is