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Sara and Kiwi are hired to do a  job of sales girl in a  showroom. Kiwi start working 2 hours after Sara. Fours hours later Sara start working, Still, 5/10 of the work is to be done. When the work is completed, the manager finds that Sara and Kiwi have done half the work. How many hours would it take each one to do the whole job individually? 

Sara and Kiwi are hired to do a  job of sales girl in a  showroom. Kiwi start working 2 hours after Sara. Fours hours later Sara start working, Still, 5/10 of the work is to be done. When the work is completed, the manager finds that Sara and Kiwi have done half the work. How many hours would it take each one to do the whole job individually?  Correct Answer 8 hrs and 4 hrs

Given∶

Kiwi start working 2 hours after Sara.

Fours hours later Sara start working.

5/10 of the work is left.

Formula Used∶

Concept of Linear Equations.

Calculation∶

Let Sara takes X hours and Kiwi takes Y hours to complete the job.

According to question;

4/x + 2y = 1 - 5/10

⇒ 4/x + 2/y = 1/2      (1)

At the end of the day, Manager found that Sara and Kiwi, They both have done the half work.

Hence, Sara spent x/2 hr., and Kiwi Y/2 hr.

And, since Sara begin 2 hours before Kiwi

x/2 - y/2 = 2

⇒ x = 4 + y             (2)

Put the value of x = 4 + y in eq.(1), we get

4/(4 + y) + 2/y = 1/2

⇒ (4y + 8 + 2y)/(y2+ 4y) = 1/2

⇒ 2(6y + 8) = (y2+ 4y)

⇒ 12y + 16 = y2+ 4y

⇒ y2- 8y + 16 = 0

⇒ y2- 4y - 4y + 16 = 0

⇒ y(y -4) - 4 (y - 4) = 0

⇒ (y - 4) (y - 4) = 0

⇒ y = 4

Put y = 4 in eq.(2)

x = 4 + 4 = 8

∴ Sara takes 8 hrs and Kiwi takes 4 hrs.

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