Maths question from Social Forest Worker exam, 2026 by JKSSB
A library has 300 rare books categorised by Fiction (F), Hardcover (H), and Best-sellers (B). There are 140 Fiction books, 120 Hardcover books, and 100 Best-sellers. 40 books are both Fiction and Hardcover, 30 are both Hardcover and Best-sellers, and 50 are both Fiction and Best-sellers. Exactly 20 books follow in all three categories. How many books are either Fiction or Hardcover, but not both, and are not Best-sellers?
Last updated Jul 21, 2026
Correct Answer:
Option C —
140
Step-by-Step Breakdown
1. Determine the Overlaps Between Categories
Items in all three categories: 20
Items in both First and Second categories: 40
Removing the twenty items that belong to all three categories leaves 20 items that belong to only the First and Second categories.
Items in both First and Third categories: 50
Removing the twenty items that belong to all three categories leaves 30 items that belong to only the First and Third categories.
Items in both Second and Third categories: 30
Removing the twenty items that belong to all three categories leaves 10 items that belong to only the Second and Third categories.
2. Find Items Belonging Exclusively to One Category
Only the First category:
Start with the total for the First category (140), then subtract those shared with only the Second category (20), those shared with only the Third category (30), and those shared across all three (20).
One hundred forty minus twenty, minus thirty, minus twenty leaves 70.
Only the Second category:
Start with the total for the Second category (120), then subtract those shared with only the First category (20), those shared with only the Third category (10), and those shared across all three (20).
One hundred twenty minus twenty, minus ten, minus twenty leaves 70.
3. Combine the Exclusive Groups
The target count consists of items belonging strictly to either the First category alone or the Second category alone:
Seventy plus seventy gives 140.
Answer verified by Quintessence Classes faculty — Karan Nagar, Srinagar.
