Maths-

General

Easy

Question

# A and B can do a piece of work in 12 days; B and C in 15 days; C and A in 20 days. How much time will A alone take to finish the work?

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: 30 days.

### 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} and work 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} 12 + W_{B} 12 = 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} 15 + W_{C} 15 = 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} 20 + W_{C} 20 = W …….(3)

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} ) =

Putting the value of W_{B} + W_{C} from equation (2)

W_{A} + = =

W_{A} =

Step 3 of 3:

Now, we can say that time taken by A to complete amount of work = 1 day

So, the time taken by A to complete W amount of work = = 30 days

Final Answer:

Hence, the time that will A alone take to finish the work is 30 days.

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