MPSC-How to solve Problems on Venn Diagram

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MPSC Examination-Learn how to solve Venn Diagram problems.

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MPSC-Problems on Venn Diagram:

MPSC-Problems on Venn Diagram MPSC-Learn how to solve Venn Problems

Using Venn Diagram solve:

Using Venn Diagram solve (1) In a survey of children , the following information was gathered: 39 children liked Mango 43 children liked Apple 56 children liked Grape 7 children liked Mango and Apple 10 children liked Mango and Grape 16 children liked Apple and Grape 4 children liked Mango , Apple, and Grape 6 children did not like any of these.

Answer the Following Questions:

Answer the Following Questions Answer the following questions: (1) How many students were surveyed? (2) How many liked Mango only? (3) How many liked Apple only? (4) How many liked Grape only?

Answer-Step-I :

Answer-Step-I Look at the problem, there are three items viz. Mango, Grape and Apple. So draw three circles like this. Mango

Answer-Step-II:

Answer-Step-II Then look at the data you have to work with. Always start with the center of the Venn diagram and work your way out. Fill in the center piece of data. As 4 Children liked Mango,Apple and Grape all so write 4 in the center. Mango 4

Answer-Step-III:

Answer-Step-III Remember, we have to compensate for the "4" in the center when calculating the numbers which are entered in the middle. Hence, 3 children liked Mango and Apple only, 12 children liked Apple and Grape only, and 6 children liked Mango and Grape only. Fill this new data into the Venn Diagram: Mango 4 3 12 6

Answer-Step-IV:

Answer-Step-IV After subtracting necessary values and inserting answers into the Venn Diagram, you should come up with the following diagram: Tips – (a) 39 children like Mango so (39-3-4-6=26) (b) 43 Children like Apple so ( 43-3-4-12=24) (c) 56 children like Grape so ( 56-6-4-12=34). Put these values in Venn diagram, we get diagram as shown Mango 4 3 12 6 26 24 34

Answer-Step-V:

Answer-Step-V The answers to the last three questions are contained explicitly in the Venn Diagram. 26 children liked Mango only, 24 children liked Apple only, and 34 children liked Grape only. For the answer to the final question, we need only add up all the children polled. Keep in mind that there were 6 children who did not like any of these. Adding all numbers ( 26+24+34+3+6+12+4+6 = 115) in the diagram plus those that did not belong in the diagram, we find that 115 children were polled in all. The final Venn Diagram would appears as shown Mango 4 3 12 6 26 24 34

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