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Quantitative Aptitude

Zonal Theorem

In a certain ...

Question

In a certain locality, 60 of the families own TV sets, 85 own scooters, 70 own fridge and 95 own radio sets.130 of the families own exactly one of these things. What is the maximum possible number of families in that locality?

A

210

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B

130

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C

220

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D

None of these

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Solution

The correct option is C 220
S = 60 + 85 + 70 + 95 = 310.

X = I + II + III + IV

S = I + 2 II + 3 III + 4 IV

S - I = 2 II + 3 III + 4 IV

310 - 130 = 180= 2 II + 3 III + 4 IV

To maximize X, make III $&$ IV=0

Then 2 II = 1800 II = 90

X max = 130+90 = 220

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