Question:medium
$X=$ Average cost price of A.C and Mobile; $Y=$ Cost price of Laptop. Decide the relation between $X$ and $Y$.
$X=$ Average cost price of A.C and Mobile; $Y=$ Cost price of Laptop. Decide the relation between $X$ and $Y$.
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Always compute CP, SP, and MP step by step, and compare the required averages only after calculating exact values for each item.
Updated On: Jul 16, 2026
- If $X > Y$
- If $X < Y$
- If $X \geq Y$
If $X \leq Y$ or can't be determined
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The Correct Option is B
Solution and Explanation
Step 1: The T.V.'s cost price is ₹30000, which is \( 60\% \) of the A.C.'s selling price, so the A.C. sells for ₹50000 and, at \( 20\% \) profit, has a cost price of ₹41666.67.
Step 2: The Laptop sells for \( 1.5 \) times the A.C.'s selling price, i.e. ₹75000, so at \( 20\% \) profit its cost price is ₹62500. This is twice the Mobile's selling price, so the Mobile sells for ₹31250 and, at \( 50\% \) profit, has a cost price of ₹20833.33.
Step 3: \( X = \) average cost price of A.C. and Mobile \( = \frac{41666.67+20833.33}{2}=₹31250 \), while \( Y = \) cost price of Laptop \( = ₹62500 \).
Step 4: Since \( 31250 \lt 62500 \), \[ \boxed{X \lt Y} \]
Step 2: The Laptop sells for \( 1.5 \) times the A.C.'s selling price, i.e. ₹75000, so at \( 20\% \) profit its cost price is ₹62500. This is twice the Mobile's selling price, so the Mobile sells for ₹31250 and, at \( 50\% \) profit, has a cost price of ₹20833.33.
Step 3: \( X = \) average cost price of A.C. and Mobile \( = \frac{41666.67+20833.33}{2}=₹31250 \), while \( Y = \) cost price of Laptop \( = ₹62500 \).
Step 4: Since \( 31250 \lt 62500 \), \[ \boxed{X \lt Y} \]
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