Brajen can paint a wall red in 10 hours while Ballari can paint h the wall completely in 12 hours. If Brajen and Ballari work alternately for an hour each starting when the wall has just cement on it till when it is completely painted red, how many hours will it take to paint the entire wall red?

Question

Question

This question was previously asked in

RRB ALP CBT I 30 Aug 2018 Shift 3 Official Paper

Answer 1

Given:

Brajen can paint a wall red in 10 hours while Ballari can paint the wall completely in 12 hours.

Brajen and Ballari work alternately for an hour each starting when the wall has just cement on it till when it is completely painted red.

Concept used:

Total work = Efficiency (Work done per hour) × Total time taken

Calculation:

Let the total work be 60 units.

Efficiency of Brajen = 60/10 = 6 units/h

Efficiency of Ballari = 60/12 = 5 units/h

In 2 hours, working alternatively they do = 6 + 5 = 11 units

In such 5 sets of 2 hours i.e. in total 10 hours, work done

⇒ 11 × 5 = 55 units

Time taken by Brajen to complete the remaining work = (60 - 55)/6 = \(\frac {5}{6}\) hours

Total time taken = 10 + \(\frac {5}{6}\) = \(10\frac {5}{6}\) hours

∴ It will \(10\frac {5}{6}\) hours to paint the entire wall red.