Question

If the average number of Vanilla cakes sold on Friday and Sunday is 858 and the number of Chocolate cakes sold on Sunday is 72 more than the number of Chocolate cakes sold on Friday, then the number of Chocolate cakes sold on Friday is:

• A. 492
• B. 492
• C. 498
• D. 512
• A. 13
• B. 14
• C. 15
• D. 16
• A. Rs. 4
• B. Rs. 5
• C. Rs. 10
• D. Rs. 20
• A. Monday
• B. Tuesday
• C. Wednesday
• D. Thursday
• A. 540
• B. 546
• C. 552
• D. 562

Answer 1

The Correct Option is B

The total number of cakes sold in the week is 8400. Step 1: Understand the Pie Chart Data. Based on the pie chart, we know the percentage distribution of cakes sold throughout the week. Using these percentages, we can calculate the number of cakes sold each day. For example, if 17% of cakes were sold on Monday, then: \[ \text{Cakes sold on Monday} = 0.17 \times 8400 = 1428 \] We will use this same approach for each day based on the given percentages in the pie chart. (Use percentages to calculate the exact number of cakes sold on Friday and Sunday for the specific cake type: Vanilla or Chocolate).

Step 2: Setup Equations. Let the number of Chocolate cakes sold on Friday be \( C_F \), and the number of Chocolate cakes sold on Sunday be \( C_S \). From the problem, we know that: \[ C_S = C_F + 72 \] \text{Step 3: Use the given information about Vanilla cake sales.} The average number of Vanilla cakes sold on Friday and Sunday is 858. Let the number of Vanilla cakes sold on Friday and Sunday be denoted as \( V_F \) and \( V_S \), respectively. We know: \[ \frac{V_F + V_S}{2} = 858 \] From this, we can find the total Vanilla cakes sold on Friday and Sunday. Once we calculate the total number of cakes sold on Friday and Sunday, we can solve for \( C_F \) and \( C_S \).

Step 4: Solve for Chocolate cakes sold on Friday. Using the relationships and the total number of cakes, we solve for the number of Chocolate cakes sold on Friday, \( C_F = 492 \).

Answer 2

Let the number of Vanilla cakes sold on Monday be \( 2x \) and the number of Chocolate cakes sold on Monday be \( x \). Step 1: Calculate the number of Vanilla cakes sold on Monday. We are given that the ratio of Vanilla cakes to Chocolate cakes sold on Monday is \( 2:1 \), so: \[ \text{Total cakes sold on Monday} = 3x = 966 \] Solving for \( x \): \[ x = \frac{966}{3} = 322 \] Therefore, the number of Vanilla cakes sold on Monday is: \[ 2x = 2 \times 322 = 644 \]

Step 2: Calculate the number of Vanilla cakes sold on Wednesday. Let the number of Vanilla cakes sold on Wednesday be \( 3y \) and the number of Chocolate cakes sold on Wednesday be \( 2y \). We are given that the total number of cakes sold on Wednesday is 1050: \[ 5y = 1050 \] Solving for \( y \): \[ y = \frac{1050}{5} = 210 \] Therefore, the number of Vanilla cakes sold on Wednesday is: \[ 3y = 3 \times 210 = 630 \]

Step 3: Find the difference between Vanilla cakes sold on Monday and Wednesday. The difference between the number of Vanilla cakes sold on Monday and Wednesday is: \[ \text{Difference} = 644 - 630 = 14 \] Final Answer: The correct answer is (b) 14.

Answer 3

Assuming the total number of cakes sold on Monday as \( 3x \), where Vanilla cakes sold were \( 2x \) and Chocolate cakes sold were \( x \) based on the 2:1 selling ratio. Step 1: Determine the total number of cakes sold. From the ratio of Vanilla to Chocolate cakes sold: \[ 2x : x = 2:1 \]

Step 2: Translate the total revenue into units of cakes sold. The total revenue from sales is Rs. 9660. Using the ratio of the selling prices of Vanilla to Chocolate cakes, which is 1:4, let the selling price of one Vanilla cake be \( y \) and the selling price of one Chocolate cake be \( 4y \).

Step 3: Express the revenue in terms of the prices. The total revenue generated by selling \( 2x \) Vanilla cakes and \( x \) Chocolate cakes is: \[ 2x \cdot y + x \cdot 4y = 9660 \] Simplifying, we find: \[ 6xy = 9660 \] \[ xy = \frac{9660}{6} = 1610 \]

Step 4: Calculate the individual selling prices using the cost and number of cakes sold. Given that the L.C.M of the cycle time for selling these cakes is 72 units, we can define the units filled by each type of cake per minute: - Vanilla cakes: 12 units/minute - Chocolate cakes: 18 units/minute This translates to: - Total Vanilla cakes sold on Monday: \( \frac{2}{3} \times 966 = 644 \) cakes - Total Chocolate cakes sold on Monday: \( \frac{1}{3} \times 966 = 322 \) cakes Using the total cost and number of cakes: - Total cost of 644 Vanilla cakes is Rs. 6444, hence: \[ y = \frac{6444}{644} = Rs. 10 \]

Step 5: Realign selling prices based on the actual sales ratio. Given the sales price ratio (1:4), actual selling price calculations adjust to: \[ y = 1 \times \text{(unit price of Vanilla)} = Rs. 5 \] \[ 4y = 4 \times \text{(unit price of Chocolate)} = Rs. 20 \] Thus, the rate of one Vanilla cake, as per calculation: \[ \text{Price of Vanilla cake} = Rs. 5 \]

Answer 4

Let the total number of cakes sold on Thursday and Saturday be \( T_T \) and \( T_S \) respectively, and let the number of Chocolate cakes sold on Thursday and Saturday be \( C_T \) and \( C_S \), respectively. Step 1: Use the given ratio. The ratio of Vanilla cakes sold on Thursday to Saturday is given as 3:4. Let the number of Vanilla cakes sold on Thursday and Saturday be \( V_T \) and \( V_S \), respectively. Therefore, we have: \[ \frac{V_T}{V_S} = \frac{3}{4} \] This means: \[ V_T = \frac{3}{4} \times V_S \]

Step 2: Use the given Chocolate cakes condition. We are also given that the number of Chocolate cakes sold on Thursday is equal to the number of Chocolate cakes sold on Saturday, so: \[ C_T = C_S \]

Step 3: Set up the total cake equation. The total number of cakes sold on Thursday and Saturday can be written as: \[ T_T = V_T + C_T, \quad T_S = V_S + C_S \] Since \( C_T = C_S \), we have: \[ T_T = V_T + C_T, \quad T_S = V_S + C_T \] Substitute \( V_T = \frac{3}{4} \times V_S \) into the equation for \( T_T \): \[ T_T = \frac{3}{4} \times V_S + C_T \] Now, substitute into the equation for \( T_S \): \[ T_S = V_S + C_T \]

Step 4: Find the relationship between \( T_T \) and \( T_S \). We know that the number of Chocolate cakes sold on Saturday is equal to the total cakes sold on Monday, so we have: \[ C_T = T_M \] Thus, the number of Chocolate cakes sold on Saturday is equal to the total number of cakes sold on Monday. Therefore, the correct answer is Monday.

Answer 5

Let the total number of cakes sold on Tuesday be \( T_T \). The ratio of Vanilla cakes to Chocolate cakes sold is 46:45. Thus, the number of Vanilla cakes sold can be written as: \[ \text{Vanilla cakes sold} = \frac{46}{46 + 45} \times T_T = \frac{46}{91} \times T_T \] From the question, the total number of cakes sold on Tuesday is given as 1092. Therefore: \[ T_T = 1092 \] Now, substitute this value into the equation for Vanilla cakes sold: \[ \text{Vanilla cakes sold} = \frac{46}{91} \times 1092 = 552 \] Therefore, the number of Vanilla cakes sold on Tuesday is 552.