Answer :

Here let’s consider that F, G, K be the families using Firewood, Gas, Kerosene for cooking respectively and no of families be U


It’s given that


No of families = n(U) = 120


Families using firewood for cooking = n(F) = 93


Families using Gas for cooking = n(G) = 45


Families using kerosene for cooking = n(K) = 63


Families using firewood and kerosene for cooking = n(F K) = 45


Families using kerosene and gas for cooking = n(KG) = 24


Families using gas and firewood for cooking = n(GF) = 27


Families using gas,kerosene and firewood for cooking = n(GKF)


Let Families using gas, kerosene and firewood for cooking = X



So from the above Venn diagram we get the following data,


People using only Gas, G’ = X – 6


People using only Kerosene K’ = X – 6


People using only firewood, F’ = 21 + X


People using only firewood and gas = (F G) – X


People using only gas and kerosene = (G K) – X = (24 – X)


People using only firewood and kerosene = (F K) – X = (45 – X)


We know that adding all the region of the Venn diagram will give the value of total number of element involved.


So, using all the data we have we can find the following


No of families = no of families using one fuel + no of families using two


Fuels + no of families using all the three fuels


Using the data obtained in the above expression we will find,


U = F’ + G’ + K’ + (F G K’) + (G K F’) + (F K G’) + X


U = F’ + G’ + K’ + (F G) – X + (G K) – X + (F K) – X + X


PUTTING ALL THE VALUES


U = 21 + X + X – 6 + X – 6 + 27 – X + 24 – X + 45 – X + X


120 = 105 – X


X = 15


Hence 15 people use all the three kind of fuel.


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