Question

Kamla and Vimla can weave a basket in 6 hours,
Vimla and Kanta can weave it in 8 hours and Kanta
and Kamla can weave it in 4 hours. How long will they
take to weave it together and each separately?​

Answer 1

It will take Kamla 12 hours, Vimla 24 hours and Kanta 16 hours to weave the basket separately.

We can use the formula:

1/T = 1/T1 + 1/T2 + 1/T3

Where T is the time taken by all three people working together, T1 is the time taken by Kamla alone, T2 is the time taken by Vimla alone and T3 is the time taken by Kanta alone.

Given that Kamla and Vimla can weave a basket in 6 hours, we know that:

1/T1 + 1/T2 = 1/6

Given that Vimla and Kanta can weave it in 8 hours, we know that:

1/T2 + 1/T3 = 1/8

Given that Kanta and Kamla can weave it in 4 hours, we know that:

1/T3 + 1/T1 = 1/4

Add all the equations together

1/T = 1/6 + 1/8 + 1/4

Solving for T, we get:

T = (864)/(8+6+4) = 24 hours

So it will take them 24 hours to weave the basket together.

To find the time taken by each person separately, we can use the same method by isolating T1, T2, T3 in the equations.

For Kamla:

1/T1 = 1/6 - 1/4

1/T1 = 1/12

T1 = 12 hours

For Vimla:

1/T2 = 1/6 - 1/8

1/T2 = 1/24

T2 = 24 hours

For Kanta:

1/T3 = 1/8 - 1/4

1/T3 = 1/16

T3 = 16 hours

So it will take Kamla 12 hours, Vimla 24 hours and Kanta 16 hours to weave the basket separately.

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