A and B together have ₹1200 . If 2/3 of A's amount is equal to 2/5 of B's amount, how much money does A have? - DSSSB - 28 August 2019 (Shift-1)

DSSSB - 28 August 2019 (Shift-1)

Non Nursing Subjects

Hard

Appeared in: DSSSB - 28 August 2019 (Shift-1)

Explanation

The problem provides two pieces of information: A + B = 1200 and (2/3)A = (2/5)B.
By rearranging the second equation, we can find the ratio of A's amount to B's amount: A/B = (2/5) / (2/3) = 3/5. So, A:B = 3:5.
The total amount is divided into 3 + 5 = 8 parts. A's share is 3 of these 8 parts.
A's amount is calculated as (3/8) of the total amount: (3/8) * 1200 = 3 * 150 = ₹450.

Option A: This value might be obtained through a calculation error, such as incorrectly determining the ratio or the value of each part. For instance, if one mistakenly assumes a 1:2 ratio (total 3 parts), A's share would be (1/3) * 1200 = ₹400.
Option B: This amount likely results from a miscalculation. For example, if one incorrectly used a ratio of 3:7 (total 10 parts), A's share would be (3/10) * 1200 = ₹360.
Option D: This value does not correspond to the correct ratio of 3:5. It might be chosen due to an arithmetic mistake during the division or multiplication steps, for example, calculating 1200/8 as 140 instead of 150, which would lead to 3 * 140 = ₹420.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Solving linear equations based on word problems involving ratios and proportions as background academic context rather than a clinical decision trigger.
This question assesses fundamental mathematical reasoning and problem-solving skills, which are essential for various calculations in a professional environment, including non-clinical tasks.
While not a clinical question, the ability to interpret relationships (like ratios) and perform accurate calculations is a foundational skill for dosage calculations, fluid balance monitoring, and interpreting lab results.
What if the question stated 2/3 of A's amount is equal to 3/5 of B's amount? The ratio would become A/B = (3/5)/(2/3) = 9/10. A's share would then be (9/19) * 1200 ≈ ₹568.42, demonstrating how the initial setup dictates the outcome.

How to Approach the Question

First, carefully read the problem to identify the given values and the relationship between them. Note that A + B = 1200 and (2/3)A = (2/5)B.
The next step is to translate the relationship into a simple ratio of A to B. Isolate the term A/B on one side of the equation.
Calculate the ratio: A/B = (2/5) / (2/3), which simplifies to A/B = 3/5. This means for every ₹3 A has, B has ₹5.
Sum the parts of the ratio (3 + 5 = 8) to determine the total number of 'shares' the total amount is divided into.
Calculate A's portion by multiplying its fraction of the total ratio (3/8) by the total amount (₹1200).
Perform the final calculation: (3/8) * 1200 = ₹450. Verify your answer by checking if it satisfies the initial conditions.

Concept Tested & Keywords

Concept Tested: Solving linear equations based on word problems involving ratios and proportions.
Stem keywords: A and B, ₹1200, 2/3 of A's amount, 2/5 of B's amount
Lead-in keywords: how much money

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