Question

Maitri and Aabhas do a work in 12 hours.

Aabhas and Kavya do the work in 15 hours.

Kavya and Maitri do
work in 20 hours.

In how many hours will they finish it together and separately?

Pls help me

Answer 1

See below ~

Explanation:

Given

• 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

Solving

• Take Maitri, Aabhas, and Kavya to be x, y, z respectively
• x + y = 12 (1)
• y + z = 15 (2)
• x + z = 20 (3)

Take Equation 1 and rewrite it so that it is equal to x.

• x = 12 - y

Take Equation 2 and rewrite it so that it is equal to z.

• z = 15 - y

Now, substitute these values in Equation 3.

• x + z = 20
• 12 - y + 15 - y = 20
• -2y + 27 = 20
• 2y = 7
• y = 7/2 = 3.5 hours [Aabhas]

Substitute the value of y in Equation 1.

• x + 3.5 = 12
• x = 8.5 hours [Maitri]

Substitute the value of y in Equation 2.

• 3.5 + z = 15
• z = 11.5 hours [Kavya]

Add the values of x, y, and z together.

• x + y + z
• 8.5 + 3.5 + 11.5
• 12 + 11.5
• 23.5 hours [together]