Question

In a pollution study of 1500 Indian canals, the following data were reported. 520 were polluted by sulphur compounds, 335 polluted by phosphate, 425 polluted by crude oil, 100 polluted by both crude oil and sulphur compounds, 180 polluted by both sulphur compounds and phosphate, 150 polluted by both phosphates and crude oil and 28 polluted by sulphur compounds, phosphates and crude oil. How many of the canals were polluted by at least one of the three impurities? How many of the canals were polluted by exactly one of the three impurities?

• A. 678, 512
• B. 768, 504
• C. 916, 496
• D. 878, 504

Answer 1

The correct option is D 878, 504

Given, sum of all impurities = S = I + 2II + 3 III = 520 + 335 + 425 = 1280 - - - (i)
III = 28 - - - (ii)
$\therefore$ I + 2 II = 1280 - 28 $\times$ 3 = 1196 - - - (iii)
Also, II + 3 III = 100 + 150 + 180 = 430 - - - (iv)
$\therefore$ II = 430 - 3 $\times$ 28 = 346
And I = 1196 - 2 $\times$ 346 = 1196 - 692 = 504
Therefore, number of canals polluted by at least one of the three impurities = X = I + II + III = 504 + 346 + 28 = 878
Number of canals polluted by exactly 1 pollutant = I = 504

Alternatively


Number of canals polluted by at least one of three impurities
= 268+152+33+72+28+122+203
= 878
Also, the number of canals polluted by exactly one of the three impurities
= 268+33+203 = 504