Question
Download Solution PDFComprehension
Four shops—A, B, C, and D—manufacture and sell items of the same kind. Shop A sold twice as many items as it left unsold. The number of items produced in Shop B is 20 more than Shop A, Shop C produced 33.33% less items as number of items produced by A. Number of unsold items in shop B is 25% more than the same in shop A. Number of sold item in shop C is 2/3rd of total unsold items of shop A and B together. Number of unsold items in shop D is double of the number of unsold items in shop C. Shop D produced 12.5% more items than number of items produced in shop C. Number of item produced in shop A is 120.
If the number of items sold by Shop F is [2/3]rd of the total number of items sold by Shop B and C together, Shop F sold 50% of items. Find the number of items produced in F?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFCommon Calculation
Shop A produced = 120
Shop A sold = 2× unsold
Let unsold = x ⇒ sold = 2x
So, total = x + 2x = 3x ⇒ 3x = 120 ⇒ x = 40, sold = 80
Shop B:
Produced = A + 20 = 120 + 20 = 140
Unsold in B = 25% more than unsold in A = 40 + 25% of 40 = 40 + 10 = 50
Sold = 140 - 50 = 90
Shop C:
Produced = 33.33% less than A = 120 - (1/3 × 120) = 120 - 40 = 80
Now:
Total unsold in A + B = 40 + 50 = 90
Sold in C = (2/3) × 90 = 60
So, Unsold = 80 - 60 = 20
Shop D:
Unsold = 2 × unsold in C = 2 × 20 = 40
Produced = 12.5% more than produced in C = 80 + 12.5% of 80 = 80 + 10 = 90
Sold = 90 - 40 = 50
|
Shop |
Total number of items produced |
Total number of items sold |
Total number of items unsold |
|
A |
120 |
80 |
40 |
|
B |
140 |
90 |
50 |
|
C |
80 |
60 |
20 |
|
D |
90 |
50 |
40 |
Calculation
Given:
Number of items sold by Shop B = 90 (from the table)
Number of items sold by Shop C = 60 (from the table)
Number of items sold by Shop F = (2/3) × (Total items sold by Shop B and C together)
Shop F sold 50% of the items it produced
Calculations:
Total items sold by Shop B and C together = 90 + 60 = 150
Number of items sold by Shop F = (2/3) × 150 = 100
Since Shop F sold 50% of the items it produced, let the total number of items produced by Shop F be x:
50% of x = 100
⇒ x = 100 × 2 = 200
The total number of items produced in Shop F is 200.
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