Maths-

General

Easy

Question

# A and B can do a piece of work in 18 days; B and C in 24 days and A and C in 36 days. In what time can they do it, all working together?

Hint:

**Hint:**

When two quantities of different units are compared and expressed as a ratio, it is known as Rate. For example, a car travels at a speed of 100 kilometres per hour, then it means in one hour it covers 100 kilometres.

## The correct answer is: 8 hours.

### Let’s say the total work is represented as W and let’s say the work done by A in 1 day is W_{A}, work done by B in 1 day is W_{B} andwork done by C in 1 day is W_{C}

Step 1 of 3:

It is given that A and B can do a piece of work in 18 days. So we can write

W_{A} 18 + W_{B} 18 = W

W_{A} + W_{B} = …….(1)

It is given that B and C can do a piece of work in 24 days. So we can write

W_{B} 24 + W_{C} 24 = W

W_{B} + W_{C} = …….(2)

It is given that A and C can do a piece of work in 36 days. So we can write

W_{A} 36 + W_{C} 36 = W

W_{A} + W_{C} = …….(3)

Step 2 of 3:

Now, adding equations (1), (2) and (3)

2(W_{A} + W_{B} + W_{C} )= + +

W_{A} + W_{B} + W_{C} = ……(4)

Step 3 of 3:

Let’s say the time taken by all of them to complete the work is t. So we can write

W_{A} t + W_{B} t + W_{C} t = W

t(W_{A} + W_{B} + W_{C}) = W

Using equation (4)

t = W

t = 16 days

Final Answer:

Hence, the time taken by all of them to complete the work is 8 hours.

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