Question

Profit rate of Paharpur Cement is more than the profit rate of Bahsin Cement in:

• A. Oct -- Dec 2008 and Jan -- Mar 2009
• B. Jan -- Mar 2009 and Apr -- Jun 2009
• C. Oct -- Dec 2008 only
• D. Jan -- Mar 2009 only
• E. Apr -- Jun 2009 only
• A. Between Jan -- Mar 2009 and Apr -- Jun 2009, profit and profit rate of Paharpur Cement increased, whereas profit and profit rate of Bahsin Cement decreased.
• B. Between Jan -- Mar 2009 and Apr -- Jun 2009, profit rate of Paharpur Cement increased but its profit decreased, whereas both profit and profit rate of Bahsin Cement increased.
• C. Between Jan -- Mar 2009 and Apr -- Jun 2009, both profit and profit rate of Paharpur Cement decreased, whereas profit rate of Bahsin Cement decreased but its profit increased.
• D. Between Jan -- Mar 2009 and Apr -- Jun 2009, profit of Paharpur Cement increased but its profit rate decreased, whereas profit rate of Bahsin Cement increased but its profit decreased.
• J. Between Jan -- Mar 2009 and Apr -- Jun 2009, profit rate of Paharpur Cement decreased but its profit increased, whereas both profit and profit rate of Bahsin Cement increased.
• A. 2.08%
• B. 2.25%
• C. 2.96%
• D. 3.28%
• O. 3.42%

Answer 1

The Correct Option is C

Step 1: Recall the formulas.
\[ \text{Profit} = (100 - x)\% \text{ of Sales Revenue} \]
\[ \text{Profit Rate} = \frac{\text{Profit}}{\text{Sales Quantity}} = \frac{(100-x)}{100} \times \text{Price} \]

Thus,
\[ \text{Profit Rate} = \frac{(100-x)}{100} \times \text{Price (Rs./bag)}. \]

Step 2: Compute profit rates for each quarter.

Oct -- Dec 2008:
For Paharpur: \(x = 92.11\), Price = 352
Profit Rate = \(\dfrac{(100 - 92.11)}{100} \times 352 = \dfrac{7.89}{100} \times 352 \approx 27.78\)
For Bahsin: \(x = 94.21\), Price = 438
Profit Rate = \(\dfrac{(100 - 94.21)}{100} \times 438 = \dfrac{5.79}{100} \times 438 \approx 25.36\)

Jan -- Mar 2009:
For Paharpur: \(x = 87.56\), Price = 304
Profit Rate = \(\dfrac{12.44}{100} \times 304 \approx 37.82\)
For Bahsin: \(x = 91.34\), Price = 440
Profit Rate = \(\dfrac{8.66}{100} \times 440 \approx 38.10\)

Apr -- Jun 2009:
For Paharpur: \(x = 91.03\), Price = 340
Profit Rate = \(\dfrac{8.97}{100} \times 340 \approx 30.50\)
For Bahsin: \(x = 89.96\), Price = 430
Profit Rate = \(\dfrac{10.04}{100} \times 430 \approx 43.17\)

Jul -- Sep 2009:
For Paharpur: \(x = 90.42\), Price = 322
Profit Rate = \(\dfrac{9.58}{100} \times 322 \approx 30.85\)
For Bahsin: \(x = 90.38\), Price = 434
Profit Rate = \(\dfrac{9.62}{100} \times 434 \approx 41.75\)

Step 3: Compare profit rates.
- Oct -- Dec 2008: Paharpur (27.78) > Bahsin (25.36)
- Jan -- Mar 2009: Paharpur (37.82) < Bahsin (38.10)
- Apr -- Jun 2009: Paharpur (30.50) < Bahsin (43.17)
- Jul -- Sep 2009: Paharpur (30.85) < Bahsin (41.75)

Thus, only in Oct -- Dec 2008, Paharpur’s profit rate is higher than Bahsin’s.

\[ \boxed{\text{Oct -- Dec 2008 only (Option C)}} \]

Answer 2

Step 1: Formula recap.
We know: \[ \text{Profit % of revenue} = 100 - \text{Cost % of revenue} \] \[ \text{Profit Rate} = \frac{\text{Profit}}{\text{Sales Quantity}} = \frac{(100 - x)}{100} \times \text{Price} \] \[ \text{Profit} = \text{Sales Quantity} \times \text{Profit Rate} \] Step 2: Compute for Jan -- Mar 2009.
- For Paharpur:
Cost % = 87.56 $\;\Rightarrow$ Profit % = $100 - 87.56 = 12.44%$
Profit Rate $= \frac{12.44}{100} \times 304 \approx 37.82$
Profit $= 543278 \times 37.82 \approx 20545470$ - For Bahsin: Cost % = 91.34 $\;\Rightarrow$ Profit % = $8.66%$
Profit Rate $= \frac{8.66}{100} \times 440 \approx 38.10$
Profit $= 526532 \times 38.10 \approx 20062975$
Step 3: Compute for Apr -- Jun 2009.
- For Paharpur:
Cost % = 91.03 $\;\Rightarrow$ Profit % = $8.97%$
Profit Rate $= \frac{8.97}{100} \times 340 \approx 30.50$
Profit $= 698236 \times 30.50 \approx 21294801$
- For Bahsin:
Cost % = 89.96 $\;\Rightarrow$ Profit % = $10.04%$
Profit Rate $= \frac{10.04}{100} \times 430 \approx 43.17$
Profit $= 499874 \times 43.17 \approx 21580560$
Step 4: Compare changes.
- Paharpur: Profit increased from $\;20545470 \to 21294801$ , but Profit Rate decreased from $37.82 \to 30.50$ .
- Bahsin: Profit increased from $\;20062975 \to 21580560$ , and Profit Rate increased from $38.10 \to 43.17$ .
Step 5: Conclude.
Thus, Paharpur saw profit increase but profit rate decrease, while Bahsin saw both profit and profit rate increase. \[ \boxed{\text{Correct Answer: (E)}} \]

Answer 3

Step 1: Recall the formula for Profit.
Profit is calculated as Profit Percentage multiplied by Price, multiplied by Sales Quantity.
The Profit Percentage is obtained by subtracting the Cost Percentage of Sales Revenue from 100.
Step 2: Write the expression for Apr -- Jun 2009.
For Apr -- Jun 2009, Cost Percentage of Paharpur Cement = 91.03.
Therefore, Profit Percentage = 100 minus 91.03 = 8.97.
Price per bag = 340.
Thus, Profit for Apr -- Jun 2009 = (8.97 divided by 100) multiplied by 340 multiplied by Sales Quantity.
Step 3: Write the expression for Jul -- Sep 2009.
For Jul -- Sep 2009, Cost Percentage of Paharpur Cement = 90.42.
Therefore, Profit Percentage = 100 minus 90.42 = 9.58.
Price per bag = 322.
Thus, Profit for Jul -- Sep 2009 = (9.58 divided by 100) multiplied by 322 multiplied by Sales Quantity for Jul -- Sep 2009.
Step 4: Relating the sales quantities.
We are told that Sales Quantity in Jul -- Sep 2009 is 2.25 percent higher than in Apr -- Jun 2009.
Let the Sales Quantity in Apr -- Jun 2009 = x.
Therefore, Sales Quantity in Jul -- Sep 2009 = x multiplied by (1 plus 2.25 divided by 100) = 1.0225 x.
Step 5: Substitution of values.
Profit in Apr -- Jun 2009 = (8.97 divided by 100) multiplied by 340 multiplied by x = 30.498 x.
Profit in Jul -- Sep 2009 = (9.58 divided by 100) multiplied by 322 multiplied by 1.0225 x.
First compute (9.58 divided by 100) multiplied by 322 = 30.84.
Now multiply this by 1.0225 to include the sales increase.
This gives approximately 31.54 x.
Step 6: Percentage increase in profit.
Increase in profit = (Profit in Jul -- Sep minus Profit in Apr -- Jun).
= (31.54 x minus 30.498 x).
= 1.042 x.
Percentage increase = (1.042 x divided by 30.498 x) multiplied by 100.
= (1.042 divided by 30.498) multiplied by 100.
= 3.42 percent.
Step 7: Conclude.
Hence, the percentage increase in profit is 3.42 percent. \[ \boxed{3.42% \text{ (Option E)}} \]