If 25 students can paint a wall in 2 hours. But at the end of every 10 mins, 10 additional students join. In how much time will the whole wall be painted?

25 students can paint the wall in 2 hours = 2 × 60 = 120 min.

⇒ part of wall painted by 25 students in one minute = 1/120

⇒ part of wall painted by 1 student in 1 min \(= \;\frac{1}{{120\; \times \;25}}\)

For the 1st 10 min, there are only 25 students

⇒ part of wall painted by 25 students in 10 min can paint \(= \;\frac{{25\; \times \;10}}{{120\; \times \;25}} = \frac{1}{{12}}\)

∴ Total part of the wall painted after 10 min = \(\frac{1}{{12}}\)

For the second span of 10 min, there are (25 + 10) = 35 students painting the wall.

⇒ part of wall painted by 35 students in 10 min \(= \;\frac{{35\; \times \;10}}{{120\; \times \;25}} = \frac{7}{{60}}\)

∴ Total part of the wall painted after 20 min = wall painted in 1st 10 min + wall painted in next 10 min

⇒ Total part of wall painted after 20 min = \(\frac{1}{{12}} + \frac{7}{{60}} = \;\frac{{12}}{{60}}\)

For the third span of 10 min, there are (35 + 10) = 45 students

⇒ part of wall painted by 45 students in 10 min \(= \;\frac{{45\; \times \;10}}{{120\; \times \;25}} = \frac{9}{{60}}\)

∴ Total part of the wall painted after 30 min = \(\frac{{12}}{{60}} + \frac{9}{{60}} = \;\frac{{21}}{{60}}\)

For the fourth span of 10 min, there are (45 + 10) = 55 students

⇒ part of wall painted by 55 students in 10 min \(= \;\frac{{55\; \times \;10}}{{120\; \times \;25}} = \frac{{11}}{{60}}\)

∴ Total part of the wall painted after 40 min = \(\frac{{21}}{{60}} + \frac{{11}}{{60}} = \;\frac{{32}}{{60}}\)

For the fifth span of 10 min, there are (55 + 10) = 65 students

⇒ part of wall painted by65 students in 10 min \(= \;\frac{{65\; \times \;10}}{{120\; \times \;25}}\; = \;\frac{{13}}{{60}}\)

∴ Total part of the wall painted after 50 min \(= \frac{{32}}{{60}} + \frac{{13}}{{60}} = \;\frac{{45}}{{60}}\)

For the 6th span of 10 min, there are (65 + 10) = 75 students

⇒ part of wall painted by 75 students in 10 min can paint \(= \;\frac{{75\; \times \;10}}{{120\; \times \;25}} = \frac{{15}}{{60}}\)

∴ Total part of the wall painted after 60 min = \(\frac{{45}}{{60}} + \frac{{15}}{{60}} = \frac{{60}}{{60}} = 1\)

The whole wall be painted in 60 min.