UPSC NDA Math Model Paper 4

Let the 19 numbers be a1,a2,a3,......,a19
Given that

a1+a2+a3+......+a19

19

=75
⇒a1+a2+a3+.....+a19 =19×75=1425 .......(1)
Also given that

a1+a2+a3+.......+a10

10

=65
⇒a1+a2+a3+.......+a10 =10×65=650 ........(2)
And

a10+a11+a12+......+a19

10

=84
⇒a10+a11+a12+.......+a19 =10×84=840 .........(3)
Adding equations (2) and (3) and subtracting equation (1) from it, we get:
a10=650+840−1425=65
Now, if a10 is excluded, the new sum will be:
left(a1+a2+a3+.........+a19)−a10 =1425−65=1360 ... from equation (1)
And the average of these 18 numbers will become 1360/18 = 75.5.