Determining data sufficiency for finding an unknown variable based on divisibility
Question
Two persons P and Q enter into a business. P puts 14,000 more than Q, but P has invested for 8 months and Q has invested for 10 months. If P's share is 400 more than Q's share out of the total profit of 2,000, what is the capital contributed by P?
Options
30,000
26,000
24,000
20,000
Explanation
Profit distribution in partnerships scales directly with the product of capital (C) and duration (T) [cite: 1414, 1415]. First, compute the individual profit shares from the total profit of ₹2,000 : P + Q = 2000 P - Q = 400 Adding the equations: 2P = 2400 \implies P = 1200, Q = 800.
The ratio of their profits is: P₍profit₎{Q₍profit₎} = 1200/800 = 3/2.
Set up the capital-time ratio: C_P × 8/C_Q × 10 = 3/2 \implies 8C_P/10C_Q = 3/2 \implies C_P/C_Q = 3/2 × 10/8 = 15/8.
Let C_P = 15x and C_Q = 8x. We know P invested ₹14,000 more than Q: 15x - 8x = 14000 \implies 7x = 14000 \implies x = 2000.
Therefore, the capital contributed by P is: 15 × 2000 = ₹30,000.
Correction validation on variables: Let's re-verify the step: 15 × 2000 = 30000. Matching option (a).
Answer: (a).
Question details
Year
2024
Paper
CSAT
Question
Q25
Section
Data Interpretation & Sufficiency
Sub-topic
Number System
Type
Statement-based
Difficulty
Medium
Source hint
Data sufficiency evaluation
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