The average weight of 10 students is increase | vedclass

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Question

(A) Let the initial average weight of $10$ students be $A \, kg$.Total initial weight $= 10A \, kg$.When a student weighing $50 \, kg$ is replaced by

Vedclass · Accepted Answer

$55$

Vedclass · Answer

(A) Let the initial average weight of $10$ students be $A \, kg$.Total initial weight $= 10A \, kg$.When a student weighing $50 \, kg$ is replaced by a new student of weight $W$,the new total weight becomes $(10A - 50 + W) \, kg$.The new average weight is $(A + 0.5) \, kg$.Therefore,the new total weight is $10(A + 0.5) = 10A + 5$.Equating the two expressions for the new total weight:$10A - 50 + W = 10A + 5$.$W - 50 = 5$.$W = 55 \, kg$.Alternatively,the increase in total weight is equal to the number of students multiplied by the increase in average weight: $10 	imes 0.5 = 5 \, kg$.Thus,the new student's weight $= 50 + 5 = 55 \, kg$.

The average weight of $10$ students is increased by $0.5 \, kg$ when one of the students weighing $50 \, kg$ is replaced by a new student. Find the weight of the new student (in $kg$).

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