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You have ‘n’ loads each of weight ‘w’. When they are weighed in pairs, the sum of weights of all the possilble pair is 120. When they are weighed in triplets, the sum of the weights of all the possible triplets is 480. find ‘n’?

You have ‘n’ loads each of weight ‘w’. When they are weighed in pairs, the sum of weights of all the possilble pair is 120. When they are weighed in triplets, the sum of the weights of all the possible triplets is 480. find ‘n’?

Grade:12

1 Answers

Riddhish Bhalodia
askIITians Faculty 434 Points
8 years ago
Choose 2 weights from n so the sum of the weights will be
\binom{n}{2}2w = n(n-1)w = 120
and when taken 3 at a time we have
\binom{n}{3}3w = n(n-1)(n-2)w/2 = 480

substitute equation 1 in equation 2 and we get
n-2 = 8 \Rightarrow n=10

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