The average weight of 5 men is decreased by 3kg when one of them weighing 150kg is replaced by another person. This new person is again replaced by another person whose weight is 30 kg lower than the person he replaced. What is the overall change in the average due to this dual change? A : 3 kg B : 9 kg C : 12 kg D : 15 kg
Solution: Total decrease in weight of 5 men = 3*5 = 15kg The weight of new Men = 150-15 = 135kg The weight of the other Men who replaces him = 135 - 30 = 105kg Total weight reduction = 150-105 = 45kg This is the total weight reduction of 5 men due to dual replacement Hence average weight reduction = 45/5 = 9 Therefore average change = 9 - 6 = 3kg ......(1)
Okay I understood all but the last line(i.e line number (1))
Let's say x is the original average of 5 men . Then the average becomes x-3 after first replacement . Further the average becomes (x-3)-6 Now ,Shouldn't the overall average change be x - [(x-3)-6] = 9kg Why this is wrong ? Please explain
Let's say weight of the persons are $x,y, z, w$ and weight of the person replacing the person of the weight 150 is $a$ kg. After first change average is decreased by $3$.
$\dfrac{x+y+z+w+150}{5}-\dfrac{x+y+z+w+a}{5}=3$
So, $a=135$. Now, $a$ is replaced by a person of weight $(a-30)$kg i.e. $105$ kg.
So, Overall change is the average is, initial average- average after replacing 150 kg person by 105 kg.
$\dfrac{x+y+z+w+150}{5}-\dfrac{x+y+z+w+105}{5}=\dfrac{45}{5}=9$
So, the answer is $9$ kg i.e option B.