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Question

Aman invited his friends to his birthday party. The birthday cake was cut into  $$12$$  pieces. John took  $$\dfrac { 1 } { 3 }$$  of the entire cake, Kapil took  $$\dfrac { 1 } { 4 }$$  of cake, Anil took  $$\dfrac { 1 } { 6 }$$  and Peter got $$\dfrac { 1 } { 6 }$$  of it. Was there any piece left of friends to come?


Solution

The cake was cut into $$12$$ pieces ; $$\Rightarrow $$ each piece is $$\dfrac { 1 }{ 12 } th$$ of whole cake John ate $$\dfrac { 1 }{ 3 } no.$$ of the cake.
Kapil took $$1/4th$$
Anil & Peter took $$4/6th$$ each of the cake
Upon adding the share's of John, Kapil, Anil & Peter we see that they have devoured $$\dfrac { 11 }{ 12 } th$$ of the cake.
$$\therefore$$   $$1/12$$ of cake is left
$$\Rightarrow 1$$ piece of cake is left.

Logical Reasoning

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