Question

A chocolate dealer has to send chocolates of three brands to a shopkeeper. All the brands are packed in boxes of the same size.
The number of boxes to be sent is 96 of brand A, 240 of brand B, and 336 of brand C.
These boxes are to be packed in cartons of the same size containing an equal number of boxes.
Each carton should contain boxes of the same brand of chocolates.
What could be the minimum number of cartons that the dealer has to send?

• A. 20
• B. 14
• C. 42
• D. 38
• E. 16
• A. increased by 6.27%
• B. decreased by 6.64%
• C. increased by 6.69%
• D. decreased by 7.11%
• J. did not change
• A. decreased by 39.15%
• B. decreased by 28.13%
• C. increased by 4.53%
• D. increased by 4.39%
• O. did not change
• A. increased by 26.57%
• B. increased by 28.12%
• C. increased by 36.19%
• D. increased by 38.16%
• T. did not change

Answer 1

The Correct Option is B

Step 1: Condition for minimum cartons.
To minimize the number of cartons, each carton should be filled to maximum capacity.
Thus, the number of boxes in each carton must be the HCF of the three numbers \(96, 240, 336\).
Step 2: Find HCF.
Prime factorization: \[ 96 = 2^5 \times 3, \quad 240 = 2^4 \times 3 \times 5, \quad 336 = 2^4 \times 3 \times 7 \] Therefore, \[ \text{HCF}(96,240,336) = 2^4 \times 3 = 48. \] Step 3: Number of cartons for each brand.
- For Brand A: \(96 \div 48 = 2\) cartons.
- For Brand B: \(240 \div 48 = 5\) cartons.
- For Brand C: \(336 \div 48 = 7\) cartons. Step 4: Total number of cartons.
\[ 2 + 5 + 7 = 14 \] Final Answer: \[ \boxed{14 \; \text{(Option B)}} \]

Answer 2

Step 1: Data from table.
- Population of Phoolgaon = 70000
- Average consumer expenditure (Jan) = Rs.47.4
- Average consumer expenditure (Mar) = Rs.49.5
- Total expenditure on roses in Jan = Rs.1136916
- Total expenditure on roses in Mar = Rs.1137915
Step 2: Total consumer expenditure (roses + carnations).
For March: \[ \text{Total expenditure (Mar)} = 49.5 \times 70000 = 3465000 \] For January: \[ \text{Total expenditure (Jan)} = 47.4 \times 70000 = 3318000 \] Step 3: Expenditure on carnations.
Carnations expenditure = Total expenditure – Rose expenditure. For March: \[ \text{Carnations (Mar)} = 3465000 - 1137915 = 2327085 \] For January: \[ \text{Carnations (Jan)} = 3318000 - 1136916 = 2181084 \] Step 4: Percentage change.
\[ %\ \text{change} = \frac{\text{Mar} - \text{Jan}}{\text{Jan}} \times 100 = \frac{2327085 - 2181084}{2181084} \times 100 \] \[ = \frac{146001}{2181084} \times 100 \approx 6.69% \] Final Answer: \[ \boxed{6.69% \; \text{increase (Option C)}} \]

Answer 3

Step 1: Extract values from table.
- Total expenditure on roses in January = Rs.1136916
- Price of roses in January = Rs.99 per dozen
- Total expenditure on roses in July = Rs.1188432
- Price of roses in July = Rs.144 per dozen
Step 2: Find number of dozens of roses sold.
Number of dozens = Expenditure / Price per dozen.
For January: \[ \text{Roses sold (Jan)} = \frac{1136916}{99} = 11484 \ \text{dozens} \] For July: \[ \text{Roses sold (Jul)} = \frac{1188432}{144} = 8253 \ \text{dozens} \] Step 3: Calculate the change in sales.
Change = July sales – January sales. \[ \Delta = 8253 - 11484 = -3231 \ \text{dozens} \] (The negative value indicates a decrease in sales.) Step 4: Percentage decrease.
\[ %\ \text{decrease} = \frac{|\Delta|}{\text{Jan sales}} \times 100 = \frac{3231}{11484} \times 100 \] \[ = 28.13% \] Step 5: Interpretation.
Since the percentage change is negative, sales in July are lower than in January by 28.13%. Final Answer: \[ \boxed{\text{Sales decreased by 28.13% (Option B)}} \]

Answer 4

Step 1: Price of carnations in January.
- Sales of carnations in January = 13848 dozens
- Average consumer expenditure on roses & carnations = Rs.47.4
- Total expenditure on both = \( 47.4 \times 70000 = 3318000 \)
- Expenditure on roses in January = Rs.1136916
- Expenditure on carnations in January = \( 3318000 - 1136916 = 2181084 \)
Therefore, \[ \text{Price of carnations (Jan)} = \frac{\text{Expenditure on carnations}}{\text{Sales of carnations}} = \frac{2181084}{13848} = 157.5 \ \text{Rs. per dozen} \] Step 2: Price of carnations in December.
- Sales of carnations in December = 18859 dozens
- Average consumer expenditure on roses & carnations = Rs.56.4
- Total expenditure on both = \( 56.4 \times 70000 = 3948000 \)
- Expenditure on roses in December = Rs.977688
- Expenditure on carnations in December = \( 3948000 - 977688 = 2970312 \)
Therefore, \[ \text{Price of carnations (Dec)} = \frac{\text{Expenditure on carnations}}{\text{Sales of carnations}} = \frac{2970312}{18859} = 157.5 \ \text{Rs. per dozen} \] Step 3: Compare January and December.
- Price in January = Rs.157.5 per dozen
- Price in December = Rs.157.5 per dozen
\[ \text{Percentage change} = \frac{\text{Dec price - Jan price}}{\text{Jan price}} \times 100 = \frac{157.5 - 157.5}{157.5} \times 100 = 0% \] Final Answer: \[ \boxed{\text{The price did not change (Option E)}} \]