Math, asked by sakshi1823, 1 year ago

sunil takes 5 days more than anil to complete a certain work. 4 days after starting tje work ,anil left the work. the remaining work was done by sunil in 5 days .find how many days each will take to complete the work.

Answers

Answered by TooFree
801

Let Anil takes x number of days to complete the work

⇒ 1 day = 1/x of the work


Sunil takes 5 more days than Anil to complete the work

⇒ x + 5 days

⇒  1 day = 1/(x + 5) of the work


Together:

1 day = 1/x + 1/(x + 5)

1 day = (x + 5 + x)/x(x+5)

1 day = (2x + 5) / (x² + 5x) of work done


Find 4 days of work done:

1 day =  (2x + 5) / (x² + 5x)

4 days = 4(2x + 5) / (x² + 5x)

4 days = (8x + 20) / (x² + 5x) of work done


Find the amount of work left to be done:

Work left = 1 -  (8x + 20) / (x² + 5x)

Work left =  (x² + 5x - 8x - 20) / (x² + 5x)

Work left = (x² - 3x - 20) / (x² + 5x)


Solve x:

Give that Anil needs 5 days to complete the rest of the work

(x² - 3x - 20) / (x² + 5x) ÷ 1/(x + 5) = 5

(x² - 3x - 20) / (x² + 5x) ×  (x + 5) = 5

(x² - 3x - 20) /x = 5

x² - 3x - 20 = 5x

x² - 8x - 20 = 0

(x - 10) (x + 2) = 0

x = 10 or x = -2 (Rejected, number of days cannot be negative)


Find the number of days each take to complete the work

Anil = x = 10 days

Sunil = x + 5 = 10 + 5 = 15 days


Answer: Anil takes 10 days and Sunil takes 15 days to complete the work.


Answered by topanswers
396

Given:

Sunil = +5 days than Anil to complete a certain work.

4 days after starting the work , Anil left the work.

Remaining work was done by sunil = 5 days

To find:

The number of days each will take to complete the work.

Solution:

The number of days taken to complete the job ( Anil ) = x

Then,

The number of days taken to complete the job ( Sunil  = x + 5

Anil in one day = 1 / x

Sunil in one day =  1 / ( x + 5 )

Working together,

For one day,

1 / x + 1 / ( x + 5 )

2x + 5 /  x ( x + 5 )

4 days together and 5 days by sunil,

4 * ( 2x + 5 ) / ( x ( x + 5 ) + 5 * 1 / ( x + 5 ) = 1

Solving for x,

We get,

x = 10

Substituting,

Hence,

Work done by Anil = 10 days

Work done by Sunil = 15 days


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