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Minena and Mashuka work together to complete a task in 9 days. Mashuka starts working alone and quits on completion of 2/5 of the work. Minena then completes the task alone. In this way, it takes 19.5 days to complete. If Mashuka works faster than Minena, how many days will Minena take to complete the task alone?

Minena and Mashuka work together to complete a task in 9 days. Mashuka starts working alone and quits on completion of 2/5 of the work. Minena then completes the task alone. In this way, it takes 19.5 days to complete. If Mashuka works faster than Minena, how many days will Minena take to complete the task alone? Correct Answer 22.5

Given:

Minena and mashuka work together complete the task in 9 days

Mashuka complete 2/5 work and minena complete 3/5 in 19.5days

Mashuka work faster than minena

Calculation:

Mashuka and minena complete work in 9 days

From option 2

Minena complete the work in 22.5days

Let the total work be 225 units

Efficiency of mashuka and minena working together = 225 / 9 = 25units/day

Efficiency of minena = 225/22.5 = 10units/day

∴ Efficiency of mashuka = 25 – 10 = 15 units/day

According to question

Mashuka completed 2/5 work = 2/5 × 225 = 90units

Mashuka takes days to complete 90units work = 90 / 15 = 6days

∴ minena complete work = 1 – 2/5 = 3/5

⇒ 3/5 × 225 = 135units

Minena takes days to complete 135units = 135 / 10 = 13.5days

Total time taken by mashuka and minena to complete the whole work in given pattern = 6 + 13.5 = 19.5days

Hence option ii satisfied the answer

Let the time taken by mashuka alone and minena alone to complete the task be 'x' and 'y' days

also (1/x + 1/y = 1/9)

⇒ x = 9y/(y - 9)    .....(i)

and (2x/5 + 3y/5 = 19.5) 

⇒ 2x + 3y = 97.5

putting value of x from equation (i). we get

⇒ 18y/(y - 9) + 3y = 97.5    

⇒ 18y + 3y2 - 27y = 97.5(y - 9)

⇒ 3y2 - 106.5y + 877.5 = 0

⇒ y2 - 35.5y + 292.5 = 0

⇒ y2 - 22.5y - 13y + 292.5 = 0

⇒ y(y - 22.5) -13(y - 22.5) = 0

⇒ y = 22.5, 13

at y = 22.5, x = 15

and at y = 13, x = 29.25 (not possible as Mashuka works faster than Minena)

∴ Minena take to complete the task alone = 22.5 days

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