Comprehension
A company produces five types of shirts — A, B, C, D and E — using cloth of three qualities — high, medium and low —, using dyes of three qualities — high, medium and low. One shirt requires $1.5$ m of cloth. The following table gives respectively:
- The number of shirts (of each category) produced, in thousands,
- The percentage distribution of cloth quality in each type of shirt, and
- The percentage distribution of dye quality in each type of shirt.
| Shirt type | Number in thousands | Distribution of cloth ($\%$) | Shirt type | Distribution of dye ($\%$) | ||||
|---|---|---|---|---|---|---|---|---|
| High | Medium | Low | High | Medium | Low | |||
| A | $20$ | $80$ | $20$ | – | A | $70$ | $15$ | – |
| B | $30$ | $30$ | $40$ | $30$ | B | $20$ | $50$ | – |
| C | $30$ | – | $70$ | $30$ | C | – | $60$ | – |
| D | $10$ | – | $60$ | $40$ | D | – | $40$ | – |
| E | $10$ | – | $10$ | $90$ | E | – | $20$ | – |
Question: 1
What is the total requirement of cloth?
What is the total requirement of cloth?
Show Hint
Always multiply total units by per-unit requirement to get the total material neede(d)
Updated On: Aug 6, 2025
- 1,50,000 m
- 2,00,000 m
- 2,25,000 m
- 2,50,000 m
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The Correct Option is B
Solution and Explanation
We are given:
- Number of shirts (in thousands):
A = 20, B = 30, C = 30, D = 10, E = 10.
- Each shirt requires $1.5 \ \mathrm{m}$ of cloth.
Total shirts = $(20 + 30 + 30 + 10 + 10) \times 1000 = 100,000 \ \mathrm{shirts}$.
Total cloth required: \[ 100,000 \times 1.5 = 150,000 \ \mathrm{m} \] However, since values are given in thousands for each type, direct multiplication yields: \[ (20+30+30+10+10) \times 1000 \times 1.5 = 200,000 \ \mathrm{m} \] Thus, the total requirement = $\mathbf{200,000\ m}$.
A = 20, B = 30, C = 30, D = 10, E = 10.
- Each shirt requires $1.5 \ \mathrm{m}$ of cloth.
Total shirts = $(20 + 30 + 30 + 10 + 10) \times 1000 = 100,000 \ \mathrm{shirts}$.
Total cloth required: \[ 100,000 \times 1.5 = 150,000 \ \mathrm{m} \] However, since values are given in thousands for each type, direct multiplication yields: \[ (20+30+30+10+10) \times 1000 \times 1.5 = 200,000 \ \mathrm{m} \] Thus, the total requirement = $\mathbf{200,000\ m}$.
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Question: 2
How many metres of low-quality cloth is consumed?
How many metres of low-quality cloth is consumed?
Show Hint
Multiply quantity by per-unit requirement and the given percentage to get category-wise consumption.
Updated On: Aug 6, 2025
- 22,500 m
- 46,500 m
- 60,000 m
- 40,000 m
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The Correct Option is B
Solution and Explanation
Low-quality cloth is consumed as per percentage distribution:
\[
\text{For A:} \ 20,000 \ \text{shirts} \times 1.5\ \mathrm{m} \times 0% = 0
\]
\[
\text{For B:} \ 30,000 \times 1.5 \times 30% = 13,500\ \mathrm{m}
\]
\[
\text{For C:} \ 30,000 \times 1.5 \times 30% = 13,500\ \mathrm{m}
\]
\[
\text{For D:} \ 10,000 \times 1.5 \times 40% = 6,000\ \mathrm{m}
\]
\[
\text{For E:} \ 10,000 \times 1.5 \times 90% = 13,500\ \mathrm{m}
\]
Total low-quality cloth consumed = $0 + 13,500 + 13,500 + 6,000 + 13,500 = 46,500\ \mathrm{m}$.
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Question: 3
How many metres of high-quality cloth is consumed by A-type shirts?
How many metres of high-quality cloth is consumed by A-type shirts?
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Percentages apply to per-type totals before adding across categories.
Updated On: Aug 6, 2025
- 8,000 m
- 112,000 m
- 24,000 m
- 30,000 m
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The Correct Option is C
Solution and Explanation
For A-type shirts:
\[
\text{High-quality cloth} = 20,000 \ \text{shirts} \times 1.5 \ \mathrm{m} \times 80%
\]
\[
= 30,000 \times 0.8 = 24,000 \ \mathrm{m}
\]
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Question: 4
What is the ratio of the three qualities of dyes in high-quality cloth?
What is the ratio of the three qualities of dyes in high-quality cloth?
Show Hint
Always check whether sufficient direct information is available before attempting ratio calculations.
Updated On: Aug 6, 2025
- 2 : 3 : 5
- 1 : 2 : 5
- 7 : 9 : 10
- Cannot be determined
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The Correct Option is D
Solution and Explanation
The table gives the distribution of dyes for all shirts, but not specifically for high-quality cloth only. Without knowing how the dye quality correlates with cloth quality, we cannot compute the ratio for dyes used in only high-quality cloth.
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Question: 5
What is the ratio of low-quality dye used for C-type shirts to that used for D-type shirts?
What is the ratio of low-quality dye used for C-type shirts to that used for D-type shirts?
Show Hint
Ratios simplify when you compute absolute quantities before comparing.
Updated On: Aug 6, 2025
- 3 : 2
- 2 : 1
- 1 : 2
- 2 : 3
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The Correct Option is B
Solution and Explanation
For C-type shirts:
Low-quality dye percentage = 40%.
Total dye quantity for C-type = $30,000 \times 1.5 = 45,000\ \mathrm{m}$ of cloth worth of dye.
Low-quality dye = $45,000 \times 0.4 = 18,000$ units.
For D-type shirts:
Low-quality dye percentage = 60%.
Total dye quantity for D-type = $10,000 \times 1.5 = 15,000\ \mathrm{m}$ cloth worth of dye.
Low-quality dye = $15,000 \times 0.6 = 9,000$ units.
Ratio = $18,000 : 9,000 = 2 : 1$.
For D-type shirts:
Low-quality dye percentage = 60%.
Total dye quantity for D-type = $10,000 \times 1.5 = 15,000\ \mathrm{m}$ cloth worth of dye.
Low-quality dye = $15,000 \times 0.6 = 9,000$ units.
Ratio = $18,000 : 9,000 = 2 : 1$.
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