A cleaning company employs 42 sweepers to clean a building in 25 days. 10 days later, 12 sweepers left the job. If the cleaning work is to be finished in 10 days, how many more cleaning workers need to be hired? A. 30 B. 32 C. 33 D. 21

A cleaning company employs 42 sweepers to clean a building in 25 days. 10 days later, 12 sweepers left the job. If the cleaning work is to be finished in 10 days, how many more cleaning workers need to be hired? A. 30 B. 32 C. 33 D. 21 Correct Answer C

Given:

The initial number of sweepers is 42

The initial number of days is 25

After 10 days 12 sweepers left.

The remaining work has to be finished in 10 days.

Concept used:

Here, we can use the unitary method

Formula used:

W₁/W₂ = (M₁D₁)/(M₂D₂)

Where W₁ is initial work, W₂ is remaining work, 

M₁ is the initial number of men, M₂ is the final number of men

D₁ is the initial number of days, D₂ final number of days

Calculation:

42 sweepers in 25 days can complete 1 unit of work

42 sweeper in 10 days can complete = (10/25) unit of work = 2/5 unit of work

So, the remaining work is = (1 - 2/5) = 3/5 unit of work

So, the remaining sweepers = (42 - 12) = 30

Now, according to the question, M₁ = 42, D₁ = 10, D₂ = 10

Let the required number of sweepers be X

So, the total number of sweeper M₂ = (30 + X)

Now, we can say

(2/5)/(3/5) = (42 × 10)/{(30 + X) × 10}

⇒ 2/3 = 42/(30 + X)

⇒ 30 + X = 63

⇒ X = 33

∴ 33 more cleaning workers need to be hired.