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The average weight of a group of 10 girls is 48 kilograms. If 2 girls R and S, replace by P and Q then the new average weight is 46 kg. The weight of P is equal to the weight of Q and the weight of R is equal to the weight of S, another girl T joins the group and the new average weight of the group becomes 46 kg. The weight of T is equal to the weight of P. What is the weight (in kg) of R?

The average weight of a group of 10 girls is 48 kilograms. If 2 girls R and S, replace by P and Q then the new average weight is 46 kg. The weight of P is equal to the weight of Q and the weight of R is equal to the weight of S, another girl T joins the group and the new average weight of the group becomes 46 kg. The weight of T is equal to the weight of P. What is the weight (in kg) of R? Correct Answer 56

Given:
Average weight of 10 girls = 48 kg

Formula:

Average weight = Sum of weight/Total members

Calculation:

Total weight of 10 girls = 48 × 10 = 480 kg

After R and S gone then P and Q join the group then the average weight = 46 kg

Now, total weight of 10 girls = 46 × 10 = 460 kg

Weight, R = S and P = Q

According to the question,

480 – 2R + 2P = 460

⇒ R – P = 10 ----(i)

After entry of T in the group, the average weight of the group remains unaffected.

⇒ Weight of T = 46 kg

Weight, T = P = 46 kg      ----(ii)

From (i) and (ii), we get

R – 46 = 10

∴ Weight of R = 56 kg

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