Question

# In a two-stage wire drawing operation, the fractional reduction (ratio of change in cross- sectional area to initial cross-sectional area) in the first stage is 0.4. The fractional reduction in the second stage is 0.3. The overall fractional reduction is

A
0.24
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B
0.58
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C
0.60
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D
1.00
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Solution

## The correct option is B 0.58Fractional reduction in first stage =Change in area in first stageOriginal area (A) before reduction 0.4=Change in area in first stageA Change in area in first stage =0.4A Area after first redirection =A−0.4A=0.6A Fraction reduction in second stage =Change in area in second stageOriginal area (A) before second stage 0.3=Change in area in second stage0.6A Change in after 2nd stage =0.18A Remaining area after 2nd reduction =0.6A−0.18A=0.42A Overall reduction in area =A−0.42A=0.58A Overall fractional reduction =Overall reduction in areaOriginal area=0.58AA=0.58

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