Question

Kittu and Vedika can complete a job in 25 days working together. Kittu alone can complete it in 35 days. Both of them worked together for 10 days and then Kittu left. Evaluate the number of days Vedika will take to complete the remaining work?

Help!

Answer 1

Given : Kittu and Vedika can complete a job in 25 days working together. Kittu alone can complete it in 35 days.

Both of them worked together for 10 days and then Kittu left.

To Find : Number of days Vedika will take to complete the remaining work

Solution:

Kittu and Vedika can complete a job in 25 days working together.

1 days work of both  = 1/25

Kittu alone can complete it in 35 days.

=> 1 day work of kittu = 1/35

=> 1 day work of vedika = 1/25 - 1/35

= (7 - 5)/175

= 2/175

1 days work of both  = 1/25

=> 10 days work of both  = 10/25  = 2/5

Work left = 1 - 2/5 = 3/5

Number of days vedika will take  = (3/5)/(2/175)

= 3 * 175 / ( 5 * 2)

= 3 * 35 / 2

= 105 /2

= 52.5

Vedika will take 52.5 days to complete the remaining work

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Answer 2

Given :-

• Kittu and Vedika can complete a job in 25 days working together.
• Kittu alone can complete it in 35 days.
• Both of them worked together for 10 days and then Kittu left.

To Find :-

• Evaluate the number of days Vedika will take to complete the remaining work ?

Solution :-

→ LCM of 25 days and 35 days = 175 units = Let total work.

so ,

→ Efficiency of (Kittu + Vedika) = Total work / Time taken = 175 / 25 = 7 units / day .

→ Efficiency of Kittu = Total work / Time taken = 175 / 35 = 5 units / day .

then,

→ Efficiency of Vedika = Efficiency of (Kittu + Vedika) - Efficiency of Kittu = 7 - 5 = 2 units / day .

now,

→ In 10 days both completes the work = Efficiency of both * 10 = 7 * 10 = 70 units .

then,

→ Left work to be done = 175 - 70 = 105 units .

therefore,

→ Time taken by Vedika to complete the remaining work = Left work / Efficiency of Vedika = 105 / 2 = 52.5 days . (Ans.)

Hence, Vedika will take 52.5 days to complete the remaining work .

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