41 girls can complete a piece of work in 40 days. If x girls started the work and after 30 days 64 more girls joined them so that the whole work gets finished in the desired time, find the value of x.

41 girls can complete a piece of work in 40 days.
x girls started the work
And after 30 days 64 more girls joined them

Concept Used:
Total work = Efficiency × Time
Here, we will take Efficiency = Number of workers
i.e Total work = Number of workers × Time

Calculation:
Total work = 41 × 40 = 1640 units

According to the question

For the second case
Total work = (x × 30) + (x + 64) × 10

So, we can write
(x × 30) + (x + 64) × 10 = 1640
⇒ 30x + 10x + 640 = 1640
⇒ 40x = 1000
⇒ x = 25

∴ The value of x is 25.