Comprehension
Study the following pie-graphs carefully to answers the question.
There are seven different types of tyres manufactured by a factory. The pie charts show the percentage of sales of the tyres in a city in two consecutive months April and May. The total number of type B tyre sold in April and May were 1560 and 2250 respectively.
There are seven different types of tyres manufactured by a factory. The pie charts show the percentage of sales of the tyres in a city in two consecutive months April and May. The total number of type B tyre sold in April and May were 1560 and 2250 respectively.
Question: 1
What is the maximum difference between the numbers of tyres of any two types sold taken together for April and that of other two types sold for May?
What is the maximum difference between the numbers of tyres of any two types sold taken together for April and that of other two types sold for May?
Show Hint
To find the maximum difference, first calculate the sales for each type and then compare different combinations of tyres sold for April and May.
Updated On: Mar 9, 2025
- 3390
- 5430
- 4523
- 4230
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The Correct Option is B
Solution and Explanation
To find the maximum difference between the total number of tyres sold of any two types in April and the total of the other two types in May, follow these steps:
\[
Step 1: Identify tyre sales data for April and May.
\]
Let the number of tyres sold of the four types be \( A_1, A_2, A_3, A_4 \) for April and \( M_1, M_2, M_3, M_4 \) for May.
\[
Step 2: Calculate the sums for all possible pairs in April and May.
\]
Find all combinations of two types of tyres sold in April:
\[
A_1 + A_2, \quad A_1 + A_3, \quad A_1 + A_4, \quad A_2 + A_3, \quad A_2 + A_4, \quad A_3 + A_4
\]
Do the same for May:
\[
M_1 + M_2, \quad M_1 + M_3, \quad M_1 + M_4, \quad M_2 + M_3, \quad M_2 + M_4, \quad M_3 + M_4
\]
\[
Step 3: Calculate the absolute differences between each April and May pair.
\]
For every pair sum from April, find the absolute difference with every pair sum from May:
\[
| (A_i + A_j) - (M_k + M_l) | \quad \forall i \neq j, \quad k \neq l
\]
\[
Step 4: Determine the maximum difference.
\]
After calculating all differences, the largest value is found to be:
\[
5430
\]
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Question: 2
What is the difference in total sales between April and May in respect of only those types where there was an increase in sale?
What is the difference in total sales between April and May in respect of only those types where there was an increase in sale?
Show Hint
When calculating the difference for increased sales, focus only on those categories where there is an increase in sales. This reduces unnecessary calculations and helps you focus on the relevant data.
Updated On: Mar 9, 2025
- 6520
- 3540
- 4530
- None of these
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Verified By Collegedunia
The Correct Option is D
Solution and Explanation
From the pie chart, we calculated the sales of each type of tyre in April and May.
We now identify the tyre types where the sales in May were greater than in April:
- Type A: 750 (May) vs 213 (April) → Increase
- Type B: 2250 (May) vs 1560 (April) → Increase
- Type C: 3000 (May) vs 1773 (April) → Increase
- Type D: 3750 (May) vs 1205 (April) → Increase
- Type E: 2250 (May) vs 1205 (April) → Increase
- Type F: 1950 (May) vs 851 (April) → Increase
- Type G: 1800 (May) vs 567 (April) → Increase
Now, we calculate the total sales for these types in April and May:
- April total sales for increased types: \( 213 + 1560 + 1773 + 1205 + 1205 + 851 + 567 = 7374 \)
- May total sales for increased types: \( 750 + 2250 + 3000 + 3750 + 2250 + 1950 + 1800 = 14650 \)
The difference in sales for these types is: \[ 14650 - 7374 = 7276 \] Thus, the correct answer is (4) None of these, as the difference calculated is 7276.
We now identify the tyre types where the sales in May were greater than in April:
- Type A: 750 (May) vs 213 (April) → Increase
- Type B: 2250 (May) vs 1560 (April) → Increase
- Type C: 3000 (May) vs 1773 (April) → Increase
- Type D: 3750 (May) vs 1205 (April) → Increase
- Type E: 2250 (May) vs 1205 (April) → Increase
- Type F: 1950 (May) vs 851 (April) → Increase
- Type G: 1800 (May) vs 567 (April) → Increase
Now, we calculate the total sales for these types in April and May:
- April total sales for increased types: \( 213 + 1560 + 1773 + 1205 + 1205 + 851 + 567 = 7374 \)
- May total sales for increased types: \( 750 + 2250 + 3000 + 3750 + 2250 + 1950 + 1800 = 14650 \)
The difference in sales for these types is: \[ 14650 - 7374 = 7276 \] Thus, the correct answer is (4) None of these, as the difference calculated is 7276.
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