Logical Reasoning Discussion

**Common Information**

After a successful T20 cricket tournament, Indian Premier League (IPL) is interested in launching a new variant of One Day International cricket called T40 (forty overs a side game). Indian Cricket League (ICL, a rival league of IPL) also has similar thoughts. An independent agency conducted a survey of 1000 respondents to determine the consumer preference of IPL versus ICL, and preference of T20 versus T40. Unfortunately, some of the survey information are lost. The following information is available:

- 70 percent of the respondents prefer T20 over T40.
- 80 percent of the respondents prefer IPL over ICL.
- 80 percent of those who preferred IPL preferred T20 over T40.

Q. |
Determine the number of respondents who prefer both T20 and ICL. |

✖ A. |
50 |

✔ B. |
60 |

✖ C. |
140 |

✖ D. |
640 |

**Solution:**

Option(**B**) is correct

Constructing the Venn diagram based on the given information, we have from the given statements:

Completing the above grid, we have:

Respondents preferring T20 and ICL = 6%, i.e. a total of 60 respondents

Hence, **option B** is the correct choice.

**Bidwattam**

*()
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In figure 2, it should be 64 and not 65.