5 class A workers and 4 class B workers are assigned a job to paint a circular park. They work for one day and complete painting till half the radius of the circular park. The next day, class B workers go on strike and returns the day after as the management resolves their problems. This creates a delay of 4 hours and 48 min in overall. If their payment is based on their efficiency, what will be the ratio of their pay?

LohaHridoy
  1. 16 : 5
  2. 5 : 16
  3. 8 : 5
  4. 5 : 8
  5. 6 : 5

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AhmedNazir

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Option 1 : 16 : 5

Let a class A worker complete the work in ‘a’ days and a class B worker complete the work in ‘b’ days

⇒ Amount of work done by a class A worker in 1 day = 1/a

⇒ Amount of work done by a class B worker in 1 day = 1/b

⇒ Amount of work done by 5 class A and 4 class B workers in 1 day = 5/a + 4/b = 1/4

⇒ 20/a + 16/b = 1 → 1

So, they would have completed the work in 4 days if the strike did not happen. But, it takes 4 days 4 hours and 48 min due to the strike

Class A workers work for 4 days 4 hours 48 min whereas class B workers work for 3 days 4 hours 48 min

⇒ 4 hours 48 min = (4/24) + {48/(60 × 24)} = 0.2 day

⇒ Total amount of work done = 4.2 × (5/a) + 3.2 × (4/a)

⇒ 1 = 21/a + 12.8/b → 2

Comparing equations 1 and 2

⇒ 21/a + 12.8/b = 20/a + 16/b

⇒ 1/a = 3.2/b

⇒ a/b = 1/3.2

Efficiency ∝ 1/Time taken

∴ Ratio of their efficiencies = 3.2 : 1 = 16 : 5
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