Average Question

Hello Experts,

Table-Based Question:::
Percentage of literate population over the total population of state for different states over the years


Year--> 1997 1998 1999 2000 2001 2002
State:
A 67 72 69 78 79 82
B 82 81 85 85 87 88
C 78 81 84 87 89 91
D 56 65 69 71 75 77
E 89 93 94 95 95 97
F 85 88 91 93 95 96

Qus: If the average population of all the states in 1999 was 12.5 lakhs. what was the average literate population in that year ?

1) 10.25 lakhs
2) 10.75 lakhs
3) 11 lakhs
4) can not be determined
5) None of these

TIL: the word lakh.

I assume "the average population of all the states in 1999" means "the total populations of states A—F in 1999." Then the average literate population cannot be determined. Indeed, imagine that every state except for A has just 100 people and the rest live in A, i.e., the population of other states is negligible compared to that of A. Then the percentage of literate population in all states is very close to 69%, and the literate population is about .69 * 12.5 lakhs. On the other hand, if every state except for E has just 100 people and the rest live in E, then the percentage of literate population in all states is very close to 94%, and the literate population is about .94 * 12.5 lakhs.

If you knew the share of each state in the total population (let's denote these numbers by a, ..., f), then the percentage of the total literate population is .69a + .85b + .84c + .69d + .94e + .91f, and the total literate population is that number times 12.5 lakhs.