If 25 students can paint a wall in 2 hour… | Answer

Subject

Quantitative Aptitude

Topic

Time and Work

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?
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ক)

40 mins

খ)

50 mins

গ)

\(53\frac{1}{3}\) mins

ঘ)

60 mins

ঙ)

55 mins

Explanation

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.

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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?Reading

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?

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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?
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