Translate a verbal age condition into an equation: Naresh’s age is 4 years less than twice the age of his brother (let brother’s age be P). Which expression correctly represents Naresh’s age?

Introduction / Context:
Algebraic translation questions require careful reading. The phrase “4 years less than twice” indicates a “twice” operation followed by a subtraction of 4 from that result.

Given Data / Assumptions:

• Brother’s present age = P.
• Naresh’s present age = ?
• Phrase: “4 years less than twice the age of his brother.”

Concept / Approach:
“Twice the age of his brother” → 2P. “4 years less than that” → subtract 4 from 2P. Hence the correct expression is 2P − 4.

Step-by-Step Solution:
1) Identify the base quantity: brother’s age P.2) Apply the multiplier: twice ⇒ 2P.3) Apply the difference: less by 4 ⇒ 2P − 4.

Verification / Alternative check:
Test with a sample: If P = 10, “twice” = 20; “4 less” = 16. The formula 2P − 4 gives 16 (consistent).

Why Other Options Are Wrong:

• 2P + 4 adds instead of subtracting.
• 4P + 2 misreads both multiplier and difference.
• P − 4 omits the “twice.”
• P + 4 ignores both “twice” and the subtraction.

Common Pitfalls:
Students frequently reverse “less than” into 4 − 2P or add 4 instead of subtracting. Read left to right but apply operations to the base quantity correctly.

Final Answer:
2P – 4