A and B together have Rs. 3000. If 2/3 of A's amount is equal to 4/9 of B's amount, how much does B have?

Appeared in: DSSSB - 29 August 2019 (Shift-1)

Explanation

The problem states (2/3)A = (4/9)B. Simplifying this gives A/B = (4/9) * (3/2) = 12/18 = 2/3. This means the amounts are in the ratio A:B = 2:3.
The total amount is Rs. 3000. This total must be divided into 5 parts (2 parts for A + 3 parts for B).
The value of each part is Rs. 3000 / 5 = Rs. 600.
B's share corresponds to 3 parts of the ratio.
Therefore, B's amount is 3 * 600 = Rs. 1800.

Option A: If B has Rs. 1500, then A also has Rs. 1500. In this case, (2/3) of A's amount is Rs. 1000, while (4/9) of B's amount is approximately Rs. 667. These are not equal, so the condition is not met.
Option B: This is the amount that A has, not B. After finding the ratio A:B = 2:3, A's share is 2 parts (2 * 600 = 1200) and B's share is 3 parts (3 * 600 = 1800). This is a common error where the calculated value for the wrong variable is chosen.
Option C: If B has Rs. 1950, then A has Rs. 1050. In this case, (2/3) of A's amount is Rs. 700, while (4/9) of B's amount is approximately Rs. 867. These are not equal.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Solving word problems involving ratios and linear equations as background academic context rather than a clinical decision trigger.
While not a clinical question, the underlying skill of ratio and proportion is critical in nursing.
Nurses use ratios daily for safe medication administration, such as calculating drug dosages (e.g., mg/kg), converting between units, and preparing solutions of a specific concentration.
Errors in these calculations can have serious patient safety consequences, making mathematical proficiency a core nursing competency.

How to Approach the Question

First, identify the key pieces of information and the relationships between them. Here, you have a total amount (A + B = 3000) and a proportional relationship ((2/3)A = (4/9)B).
Translate these verbal statements into mathematical equations. This is the most crucial step.
Solve the proportional equation to find the simplest ratio between the variables (A:B).
Use this ratio to divide the total amount into parts. Calculate the value of one 'part'.
Calculate the value for the specific variable the question asks for (in this case, B).
Double-check your answer by ensuring it satisfies both original conditions and that you have answered the specific question asked (B's amount, not A's).

Concept Tested & Keywords

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Practise the full DSSSB - 29 August 2019 (Shift-1)

Attempt every question from this paper in a timed mock, then review the full solution for each one.