A sum of Rs. 210 is to be divided among four people in the ratio 2 : 3 : 4 : 5. What are the respective amounts received by each share of this division?

Introduction / Context:
This is a straightforward ratio and proportion problem where a fixed sum of money must be divided among four parts in a given ratio. Such questions are common in aptitude tests and banking exams because they check whether a candidate can convert a verbal description of a ratio into actual numerical shares.

Given Data / Assumptions:

• Total amount to be divided = Rs. 210.
• The ratio of the four parts is 2 : 3 : 4 : 5.
• All parts are directly proportional to these ratio values.
• We assume that the entire Rs. 210 is completely divided without any remainder.

Concept / Approach:
When an amount is divided in a given ratio, each share is calculated by multiplying the total amount by the fraction corresponding to that part. The fraction for each part is its ratio number divided by the sum of all ratio numbers. So, we first find the total of the ratio terms, then compute each share of Rs. 210 using simple multiplication and division. This method generalizes to any ratio-splitting question.

Step-by-Step Solution:

Verification / Alternative check:
Add up the four shares: 30 + 45 + 60 + 75 = 210. This matches the original amount given in the question, so the division is correct and consistent with the required ratio.

Why Other Options Are Wrong:

• 30, 45, 65 and 70: These numbers do not follow the 2 : 3 : 4 : 5 ratio and the sum is 210, but middle terms break the proportional relationship.
• 35, 40, 60 and 75: The differences do not correspond to 2 : 3 : 4 : 5; the first part is too large for the given ratio.
• 30, 40, 60 and 80: The sum is 210, but the ratio of parts does not reduce to 2 : 3 : 4 : 5.

Common Pitfalls:
A common mistake is to directly divide 210 by 4 or to assume each ratio number directly equals the rupee amount. Another frequent error is to miscalculate the sum of the ratio terms, which then leads to incorrect unit value and wrong shares. Carefully adding the ratio and computing one unit correctly avoids these issues.

Final Answer:
The four amounts are 30, 45, 60 and 75 rupees respectively.