Quantitative Reasoning – Practice – How can average remain same if 5 people join or 5 people leave!!!

PSA_LEVEL-UP_QNR21. The average weight of N boys in a group is 30 kg. If 5 boys with an average weight of 12 kg join the group, the average weight would be the same as if 5 boys with an average weight of 36 kg leave the group. Find N.

(A) 15
(B) 20
(C) 25
(D) 10

Ans: In one of the case 5 boys with average weight 12 kg join the group of N while in the other 5 boys of average weight 36 kg leave the group. In either of the case , you will agree that the average weight will decrease from the original value of 30. And the final average would be same in both the case. Let us find out what is the decrease in average weight in both the cases.

When boys of average weight of 12 kg join, each of them essentially tries to reduce 18 units (30-12=18). 18 units for 5 boys amount to a reduction of 18*5 or 90 kg. This 90 kg reduction will bring about reduction in the average weight by 90/(N+5). [Note that, the number of boys increase from N to N+5].

Similarly, when boys of average weight of 36 kg leave, each of them takes away 6 units away (36-30=6).6 units for 5 boys amount to a reduction of 6*5 or 30 kg. This 30 kg reduction will bring about reduction in the average weight by 30/(N-5). [Note that, the number of boys decrease from N to N-5].

According to the question, average weight reduction is same in each case:

90/(N+5)=30/(N-5)
=> 3N-15 = N+5
=> N=10.

Alternatively, let us find the new average in each case:

In 1st case, avg weight= (30*N + 12*5) / (N+5)
In 2nd case, avg weight= (30*N – 36*5) / (N-5)

(30N+60)(N-5) =(30N-180) (N+5)
=> -150N + 60N – 300 = 150N – 180N- 900
=> 60N= 600
=> N= 10.

Although the first method looks long it is not; explanation takes bit of space but is faster compared to the second method where we had to get involved in bit more of calculations!