18 boys and 24 girls can complete a piece of work in 16 days. All of them started working together but after 12 working days, all girls and 6 boys stopped working. 12 boys completed the remaining work in 9 days. How many days will it take to complete the entire job if only 24 girls have to complete the job?

Given:

18 boys and 24 girls can complete the work in 16 days.

After 12 days, all girls and 6 boys stopped working.

Remaining 12 boys completed the remaining work in 9 days.

We need to find how many days 24 girls alone would take to complete the job.

Formula used:

Work done per day = Efficiency

Calculation:

Total work = (18 boys + 24 girls) × 16 days

Let efficiency of 1 boy = B and 1 girl = G

So, (18B + 24G) × 16 = Total work

Work done in first 12 days = (18B + 24G) × 12

Remaining work = Total work - Work done in 12 days

Remaining work = (18B + 24G) × (16 - 12)

Remaining work = (18B + 24G) × 4

This remaining work is completed by 12 boys in 9 days:

Work by 12 boys in 9 days = 12B × 9

⇒ (18B + 24G) × 4 = 12B × 9

⇒ 72B + 96G = 108B

⇒ 96G = 36B

⇒ G = (36/96)B

⇒ G = (3/8)B

Now, total work = (18B + 24G) × 16

Substituting G = (3/8)B

⇒ (18B + 24 × 3/8 B) × 16

⇒ (18B + 9B) × 16

⇒ 27B × 16

⇒ Total work = 432B

Work done by 24 girls per day = 24G

⇒ 24 × (3/8)B

⇒ 9B

Time taken by 24 girls to complete total work:

⇒ 432B / 9B = 48 days

∴ 24 girls alone will complete the work in 48 days.