Five friends, Manish, Naresh, Pavan, Salman, and Tarun, who live in the same flat, bought a cake one evening. All of them decided to eat the cake together the next morning and stored the cake in the refrigerator. However, during the night, at different times, each of the five friends sneaked to the refrigerator and ate some portion of the cake without each other’s knowledge. They did so exactly once. The next morning, the five friends found that only one-eighth of the cake was remaining.Further, it is also known thatnone of them ate more than half of the cake that was remaining at the time they went to eat the cake.Tarun ate half of the cake that was remaining when he went to eat it and Manish ate the same quantity of cake as Tarun did.Salman ate the cake after Pavan did, and after Salman finished eating, more than one-eighth of the cake was remaining.the person who ate last ate only one-fourth of the cake that was remaining when he went to eat it and Tarun ate the cake before Salman did.when Manish went to eat a portion of the cake, only four-fifths of the cake was remaining.Question:17DIRECTIONS for question 16 to 20: Select the correct alternative from the given choices.What percentage of the entire cake did Pavan eat?10%15%20%25%
Question
Five friends, Manish, Naresh, Pavan, Salman, and Tarun, who live in the same flat, bought a cake one evening. All of them decided to eat the cake together the next morning and stored the cake in the refrigerator. However, during the night, at different times, each of the five friends sneaked to the refrigerator and ate some portion of the cake without each other’s knowledge. They did so exactly once. The next morning, the five friends found that only one-eighth of the cake was remaining.Further, it is also known thatnone of them ate more than half of the cake that was remaining at the time they went to eat the cake.Tarun ate half of the cake that was remaining when he went to eat it and Manish ate the same quantity of cake as Tarun did.Salman ate the cake after Pavan did, and after Salman finished eating, more than one-eighth of the cake was remaining.the person who ate last ate only one-fourth of the cake that was remaining when he went to eat it and Tarun ate the cake before Salman did.when Manish went to eat a portion of the cake, only four-fifths of the cake was remaining.Question:17DIRECTIONS for question 16 to 20: Select the correct alternative from the given choices.What percentage of the entire cake did Pavan eat?10%15%20%25%
Solution
The problem can be solved by working backwards from the information given.
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The last person ate 1/4 of the remaining cake, which means the cake left was 1/8. So, before the last person ate, there was 1/8 / (1/4) = 1/2 of the cake.
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Before this, Salman ate some of the cake. We know that after Salman ate, more than 1/8 of the cake was remaining. Given that 1/2 of the cake was there before the last person ate, Salman must have eaten less than 1/2 - 1/8 = 3/8 of the cake.
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Before Salman, Tarun ate 1/2 of the remaining cake. So, before Tarun ate, there must have been 1/2 / (1/2) = 1 of the cake.
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Before Tarun, Manish ate the same quantity of cake as Tarun did. Given that Tarun ate 1/2 of the cake, Manish must also have eaten 1/2 of the cake. So, before Manish ate, there was 1 / (1/2) = 2 of the cake.
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Before Manish, there was 4/5 of the cake. So, the first person (Pavan) must have eaten 2 - 4/5 = 6/5 of the cake.
However, this is not possible because no one ate more than half of the cake at the time they went to eat it. Therefore, there seems to be a mistake in the problem.
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