Question

A can do 25% of a work in 4 days and B can do one thud of the same work m 4 days. C can complete the
work in the same tme as A and B would take working together. If all the three work together, how long will
take to complete the same work?​

Answer 1

Given :-

• A can do 25% of a work in 4 days .
• B can do one three of the same work in 4 days.
• C can complete the work in the same time as A and B would take working together.

To Find :-

• If all the three work together, how long will take to complete the same work ?

Solution :-

given that,

→ A can do 25% of a work in = 4 days.

So,

→ A can do 1% of a work in = (4/25) days.

than,

→ A can do 100%(total work) of a work in = (4/25) * 100 = 16 days.

Similarly, given that,

→ B can do (1/3) of a work in = 4 days.

than,

→ B can do whole work in = 4 * (3/1) = 12 days.

now, given that,

• C can complete the work in the same time as A and B would take working together.

So,

→ Time taken by C to complete whole work = 1 / {(1/16 + (1/12)} days.

Now, we have to find in how many days all three of them will complete the same work .

So,

→ per day work of A + per day work of B + per day work of C = Per day work of all three.

Putting all values we get :-

→ (1/16) + (1/12) + {(1/16) + (1/12)}

→ (1/16 + 1/16) + (1/12 + 1/12)

→ (2/16) + (2/12)

→ (1/8) + (1/6)

→ (3 + 4)/24

→ (7/24)

Hence,

→ Time taken by all three to complete total work = (24/7) days. (Ans.)

∴ If all the three work together, they will take (24/7) days to complete the same work .

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