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Five men can complete a work in 20 days. Ten women can complete the same work in 15 days. Two men and six women started working together. After 5 days, three women left the work a new man joined the work. The group continued working together till the end of the work. In how many days will they be able to do the remaining work?

Five men can complete a work in 20 days. Ten women can complete the same work in 15 days. Two men and six women started working together. After 5 days, three women left the work a new man joined the work. The group continued working together till the end of the work. In how many days will they be able to do the remaining work? Correct Answer 14

Given:

Time taken by 5 men to complete a work = 20 days

Time taken by 10 women to complete a work = 15 days

Formula used:

Work = Efficiency × Time

Calculation:

Five men can complete a work in 20 days = (20 × 5) = 100 

Ten women can complete the same work = (15 × 10) = 150 

LCM of 100 and 150 is 300

Efficiency of 1 man = (300/100) = 3 units/day

Efficiency of 1 woman = (300/150) = 2 units/day

2 men and 6 women worked together for five days

⇒ (2 × 3 + 6 × 2) × 5

⇒ (6 + 12) × 5

⇒ (18 × 5) = 90 days

Remaining work = (300 – 90) = 210 units 

Now,

After 5 days, 3 women left the work =  (6women – 3women) = 3women

And 1 man joined the work = (1man + 2man) = 3man

Time taken to complete the remaining work by 3 women and 3 men is

⇒

⇒  

⇒  

⇒ (210/15) days

⇒ 14 days

∴ The required time is 14 days

Shortcut TrickHere we need to equal number of men and women,

Ten women can complete the work in 15 days

So, five women can complete the work in 30 days

Now,

2 men and 6 women together = (2 × 3 + 6 × 2) × 5 = 90 units in five days

Remaining = 300 - 90 = 210 units

Now,

Time taken by 3 men and 3 women to complete the remaining work =  = 14 days 

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