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In the following question, two statements are numbered as Statement I and II. On solving these statements we get Quantity A and B respectively. Solve the given statements for both quantities and choose the correct option. Statement I: 5 men can finish work in 25 days. After 12 days, 2 workers have fallen sick. How much approximate time does it take to finish the work by remaining workers? Statement II: 12 men can finish a work in 28 days and 10 women can finish the same work in 30 days. What is the approximate time taken by 7 men and 5 women to finish this work?

In the following question, two statements are numbered as Statement I and II. On solving these statements we get Quantity A and B respectively. Solve the given statements for both quantities and choose the correct option. Statement I: 5 men can finish work in 25 days. After 12 days, 2 workers have fallen sick. How much approximate time does it take to finish the work by remaining workers? Statement II: 12 men can finish a work in 28 days and 10 women can finish the same work in 30 days. What is the approximate time taken by 7 men and 5 women to finish this work? Correct Answer Quantity A < Quantity B

Statement I:

Time taken by 5 men to finish a work = 25 days

Work done by 5 men in 1 day = 1/25

⇒ Work done by 1 man in 1 day = 1/25 ÷ 5 = 1/125

∴ Work done by 5 men in 12 days = 1/25 × 12 = 0.48

Work left = 1 – 0.48 = 0.52

Work done by 3 men in 1 day = 1/125 × 3 = 3/125

 Time taken by 3 men to finish the leftover work = 0.52 ÷ 3/125 = 21.67 days  22days

∴ Time taken to finish the leftover work by 3 men = 22 days

∴ Quantity A = 22 days

Statement II:

Time taken by 12 men to finish a work = 28 days

Work done by 12 men in 1 day = 1/28

Work done by 1 man in 1 day = 1/28 ÷ 12 = 1/336

Work done by 7 men in 1 day = 1/336 × 7 = 1/48

Time taken by 10 women to finish a work = 30 days

Work done by 10 women in 1 day = 1/30

Work done by 1 woman in 1 day = 1/30 ÷ 10 = 1/300

Work done by 5 women in 1 day = 1/300 × 5 = 1/60

Work done by 7 men and 5 women in 1 day = 1/48 + 1/60 = (5 + 4)/240 = 9/240 = 3/80

∴ Time taken by 7 men and 5 women to finish the work = 80/3 days = 26.66 days ≈ 27 days

∴ Quantity B = 27 days

∵ 22 < 27

∴ Quantity A < Quantity B

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