Instructions: Answer the questions based on the information given below. The Venn diagram given below shows the estimated readership of 3 daily newspapers (X, Y & Z) in a city. The total readership and advertising cost for each of these papers is as below. The total population of the city is estimated to be 14 million. The common readership (in lakhs) is indicated in the given Venn diagram. The number of people (in lakhs) who read at least one newspaper is
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Add up every separate region of the Venn diagram once each: the three only-regions, the three pairwise overlaps, and the centre.
Step 1: Read off the overlaps from the Venn diagram. Only X & Y (not Z) = 2.5 lakh, all three X, Y and Z = 0.5 lakh, only X & Z (not Y) = 1.0 lakh, only Y & Z (not X) = 1.5 lakh.
Step 2: Find how many read only X. Total readership of X is 8.7 lakh, and this total is made up of only X plus the overlaps that touch X: \( \text{only X} + 2.5 + 0.5 + 1.0 = 8.7 \), so only X \( = 8.7 - 4.0 = 4.7\) lakh.
Step 3: Find only Y and only Z the same way. For Y: \( \text{only Y} + 2.5 + 0.5 + 1.5 = 9.1 \), so only Y \( = 9.1 - 4.5 = 4.6\) lakh. For Z: \( \text{only Z} + 1.0 + 0.5 + 1.5 = 5.6 \), so only Z \( = 5.6 - 3.0 = 2.6\) lakh.
Step 4: Add up every region of the Venn diagram. At least one \( = \text{only X} + \text{only Y} + \text{only Z} + (X\cap Y) + (X\cap Z) + (Y\cap Z) + (X\cap Y\cap Z) \) \[ = 4.7 + 4.6 + 2.6 + 2.5 + 1.0 + 1.5 + 0.5 = 17.4 \]
Final Answer: 17.4 lakh people read at least one of the three newspapers, so option C is correct. \[ \boxed{17.4 \text{ lakh}} \]
