Half of the villagers of a certain village have their own houses. One-fifth of the villagers cultivate paddy. One-third of the villagers are literate. Four-fifth of the villagers are under 25 years of age. Which one of the following statements is certainly correct ?
Some villagers under 25 years of age are literate.
Given:
Half of the villagers have their own houses
One-fifth of the villagers cultivate paddy
One-third of the villagers are literate
Four-fifth of the villagers are under 25 years.
Calculation:
Let the number of villagers = x
So we have the number of villagers who
- have their own house = \(\) (1/2) x= 0.50x
- cultivates paddy = (1/5) x = 0.20x
- are literate = (1/3) x = 0.33x
- are under 25 years = (4/5) x = 0.80x
Mistake Points
statement 1 is wrong as number of villagers having their houses(0.50x) are greater than the number of literate people(0.33x).
statement 2 is certainly correct as the number of villagers under 25 years(0.80x) is greater than that the number of villagers who are literate(0.33x).
Also if we assume that both group of people are different then their sum 0.80x + 0.33x = 1.13x which is more than the number of villagers(x) itself. So, both groups will have some people in common.
statement 3 is wrong as we cannot surely say that half of the villagers who cultivates paddy are literate.
statement 4 is wrong as we can certainly say some of the villagers who have their own house are under 25 years.
Hence, option 2 is correct.
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