Discussion
Total 900 shirts were produced on Monday and Tuesday together. 5% and 4% of the shirts produced on Monday and Tuesday, respectively, were defective. If number of defective shirts produced on both the days were equal, how many shirts were produced on Tuesday ?
Answer: A
Tuesday's production was 500 shirts.
Let Monday's output be M and Tuesday's T, with \(M + T = 900\). Equal defects means \(0.05M = 0.04T\), so \(M = 0.8T\):
\[ \begin{aligned} 0.8T + T &= 900 \\ T &= 500,\quad M = 400 \end{aligned} \]
Check: 5% of 400 = 20 and 4% of 500 = 20. 400 is Monday's figure, the trap for anyone who mixes up the days.
Shortcut: equal defects means the outputs are in the inverse ratio of the defect rates, M : T = 4 : 5, so Tuesday's share is \(\frac{5}{9} \times 900 = 500\).
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