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15 girls can complete the work in 8 days while 12 boys can complete the work in 10 days. There are 8 boys started the work then 4 boys and 15 girls join them to complete the work and remaining work will be completed in 8/3 days. In what time total work gets completed?

15 girls can complete the work in 8 days while 12 boys can complete the work in 10 days. There are 8 boys started the work then 4 boys and 15 girls join them to complete the work and remaining work will be completed in 8/3 days. In what time total work gets completed? Correct Answer 8.6 days

GIVEN:

15 girls or 12 boys can complete the work in 8 days or in 10 days respectively

CALCULATION:

1 girl can complete the work in 1 day = 1/(15 × 8) = 1/120

1 boy can complete the work in 1 day = 1/(12 × 10) = 1/120

8 boys 1 days work = 8/120 = 1/15

12 boys and 15 girls 1 days work = 1/10 + 1/8 = 9/40

Fraction of work completed by 12 boys and 15 girls in 8/3 days =

⇒ (8/3) × (9/40) = 3/5

Remaining work been completed by 8 boys = 1 – (3/5) = 2/5

Time taken by 8 boys to complete 2/5th work = (2/5) × 15 = 6 days

Total time taken to complete the work = 6 + (8/3) = 8.6 days

∴ Total time taken is 8.6 days.

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