UKMT Senior Challenge-VIII

Algebra Level 4

Twenty-five workmen have completed a fifth of a project in eight days. Their foreman then decides that the project must be completed in the next 20 days. What is the smallest number of additional workmen required to complete the project on time?

This problem is not original.This problem is part of this set .

The answer is 15.

2 solutions

Meriem Kouadria
Jul 4, 2015

Work done in 8 days by 25 men: 1/5

20 days/8 days=2.5

Work done by 25 men in 20 days:2.5/5

Total work by 25 men after 28 days:3.5/5

Remaining work:1.5/5

Number of workmen required:(25x1.5)/2.5=15 workmen

Aryan Gaikwad
Mar 11, 2015

Work done by 25 men = $\frac { 1 }{ 5 }$

Therefore work left = $\frac { 4 }{ 5 }$

25 men can complete $\frac { 1 }{ 5 }$ project in 8 days

25 men can complete whole project in $8\cdot 5=40$ days

1 man can complete the whole project in $40\cdot 25=1000$ days

1 man can complete remaining project, ie $\frac { 4 }{ 5 }$ project in $\frac { 4 }{ 5 } \cdot 1000 = 800$ days

Let number of men required be $x$

Therefore, for the remaining work to be completed in 20 days, men required =

$\frac { 800 }{ 20 } =40$

Additional men required = 40 - 25 = 15

UKMT Senior Challenge-VIII

The answer is 15.

2 solutions

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