Aptitude - Average - Discussion

Can you guys tell me about what happens if the weight is decreased by 2.5 kg? Please explain.

Let the average was 10.

Then the sum of 8 people was 10*8 = 80.
When new person comes ,average was increased by 2.5 so new average is 12.5 the new sum = 12.5 * 8 = 100.

So the difference is of 20.
Now whoever new person he will increase the sum by 20 so new person weight is 65 + 20 =85 is the Answer.

By using formula,
a = r+nx ------>
a = Added value.
r = Removed value.
n = Number of persons.
x = Change in avg.

So,
a = 65+8(2.5).
a = 85 is new person weight.

Let x be an average of 8 persons.
Let y be the weight of the new person.
(x+y-65)/8 = (x/8)+2.5,
x+y-65 = x+20,
y-65 = 20,
y = 85.

Total weight of 8 persons is 520 (65*8).
Now, a total weight of 7 persons is 455 (520-65),
Now try every option to get 2.5% increase,
(455+85)/8 is equal to 67.5,
The total increase is 2.5 KG (67.5-65),
Ans is 85 KG.

Thanks for the answer. @Bhanu.

Let the average weight of 8 persons be x and the weight of first 7 persons be A.

The weight of 8 persons is A+ 65 = 8x ---> (1)
After replacing the person having weight 65, the average weight of 8 persons increased by 2.5
Now the average weight of 8 persons will be 8(x+2.5) and;

The weight of 8 persons will be A + Z(replaced person weighing 65) = 8(x+2.5) ---> (2)
Subtract (1) from (2) i.e.,
A+Z-(A+65) = 8(x+2.5) - 8x,
A+Z-A-65 = 8x + 20 -8x,
Z-65 = 20,
Z = 20+65,
Z = 85 Weight of replaced person.

Thanks @Anonymous.

Your method is good, Thanks @Bhanu.

Thanks @Bhanu.