Question

These 150 houses in a locality, out of which 60 percent have a fridge, 50 percent have a TV, and 30 percent have a swimming pool
If five of the houses have all three of these amenities and five have none, how many houses have exactly two of these amenities
​

Answer 1

Answer:

55

Step-by-step explanation:

houses having only fridge(F)= 60/100*150=90

houses having only TV(T)= 50% of 150= 75

houses having only swimming pool( S)= 30/100*150= 45

houses having all 3=5

houses having none=5

Total houses = number with fridge + number with TV + number with pool - number with only two of the three things - 2(number with all three things) + number with none of the three things

150=90+75+45-number with only two of the three things-2*5+5

number with only two=210+5-10-150

number with only two= 55

Answer 2

Given : These 150 houses in a locality, out of which 60 percent have a fridge, 50 percent have a TV, and 30 percent have a swimming pool

 five of the houses have all three of these amenities and five have none

To Find :  how many houses have exactly two of these amenities ​

Solution:

Fridge  F = (60/100)150 = 90

TV  T   = (50/100)150  = 75

Swimming Pool  S = (30/100)150  = 45

All three F ∩ T ∩ S = 5

None  = 5

Total = F + T + S  -   F ∩ T  -  F ∩  S -   T ∩ S  +  F ∩ T ∩ S + None

=> 150 = 90 + 75 + 45 - ( F ∩ T +  F ∩  S +    T ∩ S) + 5 + 5

=> 70 =  F ∩ T +  F ∩  S +    T ∩ S

exactly two of these amenities = F ∩ T +  F ∩  S +    T ∩ S - 3 F ∩ T ∩ S

= 70 - 5* 3

= 55

55  houses have exactly two of these amenities

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