M4maths Previous Puzzles

16 Sep 2022 Average

Shubhendu was asked to find the average of first 'n' natural numbers. By mistake, he added a number twice but he didn’t noticed it. As a result, he obtained a wrong average of 31.3. Find the number he added twice?

OPtion

1) 52
2) 36
3) 42
4) 54
5) 45
6) 48
7) 62
8) 49
9) 47
10) None of these

Solution

Sum of first 'n' natural numbers = n(n+1)/2
.'. Their average = [n(n+1)/2]/n = (n+1)/2
Given, average is 31.3 including one number twice.
As we know average lies some way at middle of sum of first 'n' natural numbers.
So check for the average of first 60 numbers = (60+1)/2 = 30.5
Given, average 31.3 is 0.8 more than the average of first 60 number including one number twice.
So, number repeated twice = 0.8x60 = 48
Correct Option 6)

Correct Option: 6 Best Solution (1)

G.S.Kantharao   2 years AGO

Here new mean =31.3
Average of n naturals=n(n+1)/2n=(n+1)/2
So it might be 30.5 or 31
If it is 31 then n+1/2=31=n=61
So the diff average =0.3
Sum is 0.3*61=18.3 is not a natural number.
So consider 30.5
Now n+1/2=30.5=>n=60
So difference=0.8
Sum =0.8*60=48
So 48 is added twice.
My option is 6 👈

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