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The average weight of A, B and C is 45 kg. If the average weight of A and B be 40 kg and that of B and C be 43 kg, then the weight of B is:
26 kg
31 kg
19 kg
23 kg
31 kg
Calculate the sum of all: (A+B+C) = 135. Calculate (A+B) = 80 and (B+C) = 86. Add (A+B) and (B+C) to get A+2B+C = 166. Subtract (A+B+C) from (A+2B+C) to find B = 166 - 135 = 31.
Average weight of (A, B, C) = 45 kg, Average weight of (A, B) = 40 kg, Average weight of (B, C) = 43 kg.
Sum=Average├Чn
Calculate the sum of all: (A+B+C) = 135. Calculate (A+B) = 80 and (B+C) = 86. Add (A+B) and (B+C) to get A+2B+C = 166. Subtract (A+B+C) from (A+2B+C) to find B = 166 - 135 = 31.
A common mistake is assuming that (A+B) + (B+C) equals (A+B+C) instead of (A+2B+C), which leads to an incorrect value for B.
Calculate sum of weights
Since the average weight of A, B, and C is 45 kg, their total weight is 3├Ч45=135 kg.
A+B+C=135
Calculate partial sums
Given the average of A and B is 40 kg, their total is 2├Ч40=80 kg. Given the average of B and C is 43 kg, their total is 2├Ч43=86 kg.
A+B=80,B+C=86
Determine weight of B
Adding the two partial sums: (A+B)+(B+C)=80+86, which simplifies to A+2B+C=166. Subtracting (A+B+C=135) from this gives B=166тИТ135=31 kg.
B=166тИТ135=31
B is correct because calculating the sum of the partial weights (A+B) and (B+C) and subtracting the total weight (A+B+C) results in 31 kg.
This type of overlapping set problem is common in Quantitative Aptitude; always look for the middle term that is counted twice.
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