Question

$X=$ Average profit amount of all items; $Y=$ Average discount amount of all items. 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:

When comparing averages, calculate the sum of all profits and discounts separately, then divide by the number of items before comparing.

Answer 1

The Correct Option is B

Using the values computed in Q6: 
Profits (SP–CP): 
AC: ₹ \(50000-41666.\overline{6}=8333.\overline{3}\) 
TV: ₹ \(36000-30000=6000\) 
Cooler: ₹ \(15000-13636.\overline{36}=1363.\overline{63}\) 
Mobile: ₹ \(31250-20833.\overline{3}=10416.\overline{6}\) 
Laptop: ₹ \(75000-62500=12500\) 
\[\text{Sum profit} = ₹38613.\overline{63}, \quad X = \frac{38613.\overline{63}}{5} \approx ₹7722.73\]  
Discounts (MP–SP): 
AC: ₹ \(62500-50000=12500\) 
TV: ₹ \(60000-36000=24000\) 
Cooler: ₹ \(18750-15000=3750\) 
Mobile: ₹ \(41666.\overline{6}-31250=10416.\overline{6}\) 
Laptop: ₹ \(107142.\overline{85}-75000=32142.\overline{85}\) 
\[\text{Sum discount}  \approx ₹82809.52, \quad Y = \frac{82809.52}{5} \approx ₹16561.90\]