Maths-

General

Easy

Question

# A, B and C can reap a field in 15 ¾ days; B, C and D in 14 days; C, D and A in 18 days; D, A and B in 21 days. In what time can A, B, C and D together reap it?

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: 12 3/5 days

### Let’s say the total work done to reap the field 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},work done by C in 1 day is W_{C} and work done by D in 1 day is W_{D}

Step 1 of 3:

It is given that A, B and C can reap a field in 15 ¾ days or 15.75 days. So we can write

W_{A} 15.75 + W_{B} 15.75 + W_{C} 15.75 = W

W_{A} + W_{B} + W_{C} = …….(1)

It is given that B, C and D can reap a field in 14 days. So we can write

W_{B} 14 + W_{C} 14 + W_{D} 14 = W

W_{B} + W_{C} + W_{D} = …….(2)

It is given that C, D and A can reap a field in 18 days. So we can write

W_{C} 18 + W_{D} 18 + W_{A} 18 = W

W_{C} + W_{D} + W_{A} = …….(3)

It is given that D, A and B can reap a field in 21 days. So we can write

W_{C} 21 + W_{D} 21 + W_{A} 21 = W

W_{D} + W_{A} + W_{B} = …….(4)

Step 2 of 3:

Now, adding equations (1), (2), (3) and (4)

3(W_{A} + W_{B} + W_{C} + W_{D}) =

W_{A} + W_{B} + W_{C} + W_{D} = ……(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_{D} t = W

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

Using equation (4)

t = W

t = days = 12 days.

Final Answer:

Hence, the time taken by A, B, C and D together to reap the field is 12 days.

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