Language distribution in a class of 60: 30% speak only English, 20% speak both Hindi and English, and the rest speak only Hindi. How many children can speak Hindi?

Introduction / Context:This is a basic set-partition problem with percentages. We partition the class into mutually exclusive groups: only English, both languages, and only Hindi, then count Hindi speakers (both + only Hindi).

Given Data / Assumptions:

• Total children = 60.
• Only English = 30% of 60.
• Both Hindi and English = 20% of 60.
• Remaining are only Hindi.

Concept / Approach:Compute counts for “only English” and “both,” subtract from total to get “only Hindi.” Hindi speakers = both + only Hindi. Each group is disjoint and covers the class.

Step-by-Step Solution:Only English = 0.30 * 60 = 18Both = 0.20 * 60 = 12Only Hindi = 60 − 18 − 12 = 30Hindi speakers = both + only Hindi = 12 + 30 = 42

Verification / Alternative check:Sum of groups: 18 + 12 + 30 = 60, consistent partition.

Why Other Options Are Wrong:36, 30, 48, 40 miscount either the “both” group or the complements leading to incorrect totals of Hindi speakers.

Common Pitfalls:Adding “both” to “only English” or double-counting those who speak both languages.

Final Answer:42