Deducing logical conclusions from standard categorical syllogisms
Question
A person buys three articles P, Q and R for 3,330. If P costs 25% more than R and R costs 20% more than Q, then what is the cost of P? [cite: 1806, 1807, 1808]
Options
1,000
1,200
1,250
1,350
Explanation
Set up a backward chain of variable expressions starting with article Q. Let the cost of Q = x. R costs 20\% more than Q: R = 1.2x. P costs 25\% more than R: P = 1.25 × R = 1.25 × 1.2x = 1.5x.
We know the total cost of all three articles combined is ₹3,330: P + Q + R = 3330 1.5x + x + 1.2x = 3330 \implies 3.7x = 3330.
Solve for x: x = 3330/3.7 = 33300/37 = 900.
Now, calculate the specific cost of article P: P = 1.5 × 900 = 1350.
Answer: (d).
Question details
Year
2024
Paper
CSAT
Question
Q47
Section
Logical & Analytical Reasoning
Sub-topic
Syllogism
Type
Statement-based
Difficulty
Easy
Source hint
Syllogism statements and conclusions
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