Question

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 together and separately?​

Answer 1

Answer:

Work done by Maitri and Abhas in 1 hour = 1/12

Work done by Abhas and Kavya in 1 hour = 1/15

Work done by Kavya and Maitri in 1 hour = 1/20

Add the numbers

Maitri and Abhas + Abhas and Kavya + Kavya and Maitri=

1/12 + 1/15 + 1/20

=1/5

2(Maitri + Abhas + Kavya) = 1/5

Maitri + Abhas + Kavya = 1/5 × 1/2 = 1/10th of work in 1 day

Therefore, Maitri, Abhas and Kavya do the work together in 10 days.

Now add

Maitri and Abhas + Maitri and Kavya= 1/12 + 1/20 = 8/60

2(Maitri) + Kavya and Abhas

It is given that Kavya and Abhas do the work together in 15 hours.

So Subtract it from 8/60

8/60-1/15 = 4/60 = 1/15

1/15 × 1/2 = 1/30.

Maitri do the work in 30 hours

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Work done by Maitri and Abhas in 1 hour = 1/12

Work done by Abhas and Kavya in 1 hour = 1/15

Work done by Kavya and Maitri in 1 hour = 1/20

Add the numbers

Maitri and Abhas + Abhas and Kavya + Kavya and Maitri=

1/12 + 1/15 + 1/20

=1/5

2(Maitri + Abhas + Kavya) = 1/5

Maitri + Abhas + Kavya = 1/5 × 1/2 = 1/10th of work in 1 day

Therefore, Maitri, Abhas and Kavya do the work together in 10 days.

Now add

Maitri and Abhas + Maitri and Kavya= 1/12 + 1/20 = 8/60

2(Maitri) + Kavya and Abhas

It is given that Kavya and Abhas do the work together in 15 hours.

So Subtract it from 8/60

8/60-1/15 = 4/60 = 1/15

1/15 × 1/2 = 1/30.

Maitri do the work in 30 hours

Do the same process for others.

ahlukileoi and 7 more users found this answer helpful

THANKS

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Answer 2

Answer:

• 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