Question

$X=$ Average cost price of A.C and Mobile; $Y=$ Cost price of Laptop. Decide the relation between $X$ and $Y$. 

• A. If $X > Y$
• B. If $X < Y$
• C. If $X \geq Y$
• D. If $X \leq Y$ or can't be determined

Hint:

Always compute CP, SP, and MP step by step, and compare the required averages only after calculating exact values for each item.

Answer 1

The Correct Option is B

From the paragraph: 
- TV: discount $40\%$, profit $20\%$, discount amount ₹24000 $\Rightarrow$ MP\(_{TV}\)=₹60000, SP\(_{TV}\)= ₹36000, CP\(_{TV}\)= ₹30000. 
- AC: “20\% profit after 20\% discount” $\Rightarrow$ SP\(_{AC}\)=1.2 CP\(_{AC}\). Also CP\(_{TV}\)=0.6 SP\(_{AC}\)$\Rightarrow$ SP\(_{AC}\)=₹ 50000, hence CP\(_{AC}\)=₹41666.\(\overline{6}\). 
- Cooler: SP is $50\%$ of CP\(_{TV}\)$\Rightarrow$ SP\(_{Cool}\)=₹15000. Given profit $10\%$ and discount $20\%$: CP\(_{Cool}\)=SP/1.1=₹13636.\(\overline{36}\); MP\(_{Cool}\)=SP/0.8=₹18750. 
- Laptop: SP is $50\%$ more than SP\(_{AC}\) and profit is $20\%$ $\Rightarrow$ SP\(_{Lap}\)=₹75000, CP\(_{Lap}\)=SP/1.2=₹62500 (and since discount $30\%$, MP\(_{Lap}\)=₹107142.\(\overline{85}\)). 
- Mobile: Laptop CP is twice Mobile SP $\Rightarrow$ SP\(_{Mob}\)=₹31250; also profit $50\%$ with $25\%$ discount $\Rightarrow$ CP\(_{Mob}\)=SP/1.5=₹20833.\(\overline{3}\); MP\(_{Mob}\)=SP/0.75=₹41666.\(\overline{6}\). 
 

Answer 2

Here \( X \) is the average cost price of the A.C. and the Mobile, and \( Y \) is the cost price of the Laptop. Each cost price can be built up from the T.V.'s figures using ratio multipliers instead of straight percentage arithmetic.

The T.V.'s discount is \( 40\% \), amounting to ₹24000, i.e. \( \frac{2}{5} \) of the marked price, so the marked price is \( 24000 \times \frac{5}{2} = ₹60000 \) and the selling price is \( 60000 \times \frac{3}{5} = ₹36000 \). At a \( 20\% \) profit, the cost price of the T.V. is \( 36000 \times \frac{5}{6} = ₹30000 \).

The T.V.'s cost price is \( 60\% \) of the A.C.'s selling price, so the A.C.'s selling price is \( 30000 \times \frac{5}{3} = ₹50000 \). At a \( 20\% \) profit, the cost price of the A.C. is \( 50000 \times \frac{5}{6} = ₹41666.67 \).

The Laptop sells for \( 50\% \) more than the A.C.'s selling price, i.e. \( 50000 \times \frac{3}{2} = ₹75000 \), and at a \( 20\% \) profit its cost price is \( 75000 \times \frac{5}{6} = ₹62500 \).

The Laptop's cost price is twice the Mobile's selling price, so the Mobile's selling price is \( 62500 \div 2 = ₹31250 \). At a \( 50\% \) profit, the cost price of the Mobile is \( 31250 \times \frac{2}{3} = ₹20833.33 \).

So \( X = \frac{41666.67 + 20833.33}{2} = ₹31250 \) and \( Y = ₹62500 \). Now check each option:

1. If \( X \gt Y \): This needs \( 31250 \gt 62500 \), which is false.
2. If \( X \lt Y \): Since \( 31250 \lt 62500 \), this statement holds true.
3. If \( X \geq Y \): This needs \( 31250 \geq 62500 \), which is false.
4. If \( X \leq Y \) or can't be determined: Although \( X \leq Y \) is numerically true, the relation is fully determinable and is expressed more precisely by \( X \lt Y \), so this is not the best-fitting choice.

The relation that holds precisely is \( X \lt Y \).

So, the correct answer is If \( X \lt Y \).