Maitri and aabhas do a work in 12 hours. Aabhas And Kavya do the work in 15 hours. Kavya and Maitri do the work in 20 hours. In how many hours will they finish it and together?
Answers
Maitri and Aabhas (M + A) = 12 hours
Aabhas and Kavya (A + K) = 15 hours
Kavya and Maitri (K + M) = 20 hours
Let they can together finish the work in x days, and we need to Multiply capacity of each by 2, as we are adding both twice.
(m + a) = 12 hours × 2 = 24 hours
(a + k) = 15 hours × 2 = 30 hours
(k + m) = 20 hours × 2 = 40 hours
• They can finish work together in :
⇒ x/(m + a) + x/(a + k) + x/(k + m) = Total Work
⇒ x/24 + x/30 + x/40 = 1
⇒ (5x + 4x + 3x)/120 = 1
⇒ 12x/120 = 1
⇒ x/10 = 1
⇒ x = 10 hours
∴ They can finish work together in 10 hours.
⠀⠀⠀⠀⠀───────────────
• Each can finish work separately in :
⇢ Kavya = (m + a)•x/(m + a) - x
⠀⠀⠀⠀⠀⠀= 12•10/(12 - 10)
⠀⠀⠀⠀⠀⠀= 120/2
⠀⠀⠀⠀⠀⠀= 60 hours
⇢ Maitri = (a + k)•x/(a + k) - x
⠀⠀⠀⠀⠀⠀= 15•10/(15 - 10)
⠀⠀⠀⠀⠀⠀= 150/5
⠀⠀⠀⠀⠀⠀= 30 hours
⇢ Aabhas = (k + m)•x/(k + m) - x
⠀⠀⠀⠀⠀⠀⠀= 20•10/20 - 10
⠀⠀⠀⠀⠀⠀⠀= 200/10
⠀⠀⠀⠀⠀⠀⠀= 20 hours