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
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