Question

A group of 30 workers can complete a piece of work in 21 days. How many workers should be added to complete the work in 14 days.

Answer 1

Given that,

• A group 30 workers can complete a piece of work in 21 days.

.

To Find,

• How many workers should be added to complete the work in 14 days ?

.

Solution,

Let the Total work be 1.

As we know,

• Capacity = Work / Time

The capacity of 30 workers is 1/21.

The capacity of each worker is 1/630 [1/21 ÷ 30 = 1/630].

Let the number of added workers be 'x'.

Now, The Time should be 14 days.

The Capacity of all together is 1/14.

The expression should be,

$\boxed{ \text{30 worker's capacity} + \text{No. of Added Workers}( \text{Each worker's capacity}) = \text{All worker's Capacity}}$

Simplifying the expression,

$:\longrightarrow \frac{1}{21} + x \bigg( \frac{1}{630} \bigg ) = \ \frac{1}{14} \\ \\ :\longrightarrow \frac{1}{21} + \frac{x}{630 } = \frac{1}{14} \\ \\ :\longrightarrow \frac{30 + x}{630} = \frac{1}{14} \\ \\ :\longrightarrow x + 30 = \frac{630}{14} \\ \\ :\longrightarrow x + 30 = 45 \\ \\ :\longrightarrow \boxed{x = 15}$

Hence, The value of 'x' is 15.

Therefore, 15 workers should be added.

.

Required Answer,

• 15 workers should be added to complete the piece of work in 14 days.