Question

The number of people (in lakhs) who read at least one newspaper is

• A. 4.7
• B. 11.9
• C. 17.4
• D. 23.4
• A. 4.7
• B. 11.9
• C. 17.4
• D. 23.4

Answer 1

The Correct Option is C

Given data (in lakhs):
• Readership totals: |X| = 8.7, |Y| = 9.1, |Z| = 5.6.
• Venn (pairwise-only & triple): X∩Y only = 2.5, Y∩Z only = 1.5, X∩Z only = 1.0, and X∩Y∩Z = 0.5.

Step 1 — Express each paper’s total as disjoint regions:
|X| = (only X) + (X∩Y only) + (X∩Z only) + (X∩Y∩Z).
|Y| = (only Y) + (X∩Y only) + (Y∩Z only) + (X∩Y∩Z).
|Z| = (only Z) + (X∩Z only) + (Y∩Z only) + (X∩Y∩Z).

Step 2 — Solve for “only” regions using the totals:
only X = 8.7 − (2.5 + 1.0 + 0.5) = 8.7 − 4.0 = 4.7.
only Y = 9.1 − (2.5 + 1.5 + 0.5) = 9.1 − 4.5 = 4.6.
only Z = 5.6 − (1.0 + 1.5 + 0.5) = 5.6 − 3.0 = 2.6.

Step 3 — Compute “at least one” (= union) by adding all disjoint regions:
|X ∪ Y ∪ Z| = (only X) + (only Y) + (only Z) + (X∩Y only) + (Y∩Z only) + (X∩Z only) + (X∩Y∩Z).
= 4.7 + 4.6 + 2.6 + 2.5 + 1.5 + 1.0 + 0.5.
Add sequentially for clarity:
4.7 + 4.6 = 9.3 → 9.3 + 2.6 = 11.9 → 11.9 + 2.5 = 14.4 → 14.4 + 1.5 = 15.9 → 15.9 + 1.0 = 16.9 → 16.9 + 0.5 = 17.4.

Step 4 — Quick inclusion–exclusion check (conceptual):
When pairwise entries are “only” overlaps, the union is simply the sum of all seven disjoint regions; that’s exactly what we computed above, confirming no double counting.

Final Answer: 17.4 lakhs (matches option (C)).

Answer 2

Goal: Find the number of people (in lakhs) who read only one of the newspapers X, Y, Z.

Given (from the Venn and table, all in lakhs):
|X| = 8.7, |Y| = 9.1, |Z| = 5.6.
X∩Y only = 2.5, Y∩Z only = 1.5, X∩Z only = 1.0, X∩Y∩Z = 0.5.

Step 1 — Express totals as disjoint-region sums:
|X| = (only X) + (X∩Y only) + (X∩Z only) + (X∩Y∩Z).
|Y| = (only Y) + (X∩Y only) + (Y∩Z only) + (X∩Y∩Z).
|Z| = (only Z) + (X∩Z only) + (Y∩Z only) + (X∩Y∩Z).

Step 2 — Solve the “only” regions:
only X = 8.7 − (2.5 + 1.0 + 0.5) = 8.7 − 4.0 = 4.7.
only Y = 9.1 − (2.5 + 1.5 + 0.5) = 9.1 − 4.5 = 4.6.
only Z = 5.6 − (1.0 + 1.5 + 0.5) = 5.6 − 3.0 = 2.6.

Step 3 — Add the exactly-one readers:
Total (only one) = (only X) + (only Y) + (only Z) = 4.7 + 4.6 + 2.6 = 11.9 lakhs.

Answer: 11.9 lakhs (matches option (B)).