Math, asked by hemant5393, 1 year ago

Tarun , Teja and Rafeek set out to complete a work . Rafeek being the eldest would take 1 day less than Tarun if he were to complete the work alone All three together could complete the Work in a day . However , Rafeek was kidnapped by Gabbar . Tarun and Teja began the work in his absence . After a day , Tarun was also kidnapped . Teja took 3 more days to finish the work . How much portion of the work Rafeek could do in a day ?​

Answers

Answered by amitnrw
0

Answer:

1/2

Step-by-step explanation:

Tarun , Teja and Rafeek set out to complete a work . Rafeek being the eldest would take 1 day less than Tarun if he were to complete the work alone All three together could complete the Work in a day . However , Rafeek was kidnapped by Gabbar . Tarun and Teja began the work in his absence . After a day , Tarun was also kidnapped . Teja took 3 more days to finish the work .

Let say rafeek complete work in R days

Rafeek 1 day work = 1/R

Rafeek being the eldest would take 1 day less than Tarun

Tarun complete work in R + 1 day

Tarun's 1 day work = 1/(R + 1)

All three together could complete the Work in a day

Teja 1 day work =  1  - 1/R - 1/(R+1)

= (1/R(R+1))( R² + R - R - 1 - R)

= (R² - R - 1)/R(R+1)

Tarun and Teja  1 day work = 1 - 1/R = (R -1)/R

Teja 3 day work  = 3 (R² - R - 1)/R(R+1)

(R -1)/R + 3 (R² - R - 1)/R(R+1)  = 1

=> (R -1)(R+1)  + 3(R² - R - 1) = R(R+1)

=> R² - 1 + 3R² - 3R - 3 = R² + R

=> 3R² - 4R - 4 = 0

=> 3R² - 6R + 2R - 4 = 0

=> 3R(R - 2) + 2(R -2) = 0

=> (3R + 2)(R - 2) = 0

=> R = 2   ( as R can not be -ve)

1/R = 1/2

Rafeek could do in a day = 1/2 portion of work

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