Question

15 men build a 16.25 m long wall up to a certain height in one day. How many men should be employed to build a wall of the same height but of length 26 meters in one day?

Answer 1

Hint: First, find the number of men required to build a wall of 26m in one day. Then, find the length of the wall built by 1 man in a day. Then, the product of the total number of men required and the wall built by 1 man in a day is equal to the length of the wall to be built.

Complete step-by-step answer:
Given: - 15 men can build a 16.25 m wall in a day.
Let, the number of men required to build a wall of 26m in one day be x.
Now find the length of the wall build by a man in a day,
$\dfrac{{16.25}}{{15}}m$
The product of the total number of men required and the wall built by 1 man in a day is equal to the length of the wall to be built.
$x \times \dfrac{{16.25}}{{15}} = 26$
Multiply both sides by $\dfrac{{15}}{{16.25}}$,
$x \times \dfrac{{16.25}}{{15}} \times \dfrac{{15}}{{16.25}} = 26 \times \dfrac{{15}}{{16.25}}$
Cancel out the common factors from the numerator and denominator from both sides of the equation,
$x = 2 \times 12$
Multiply the terms on the right side to get the result,
$x = 24$

Hence, the number of men required to build a wall of 26m in one day is 24.

Note: Alternative method 15 men can build a 16.25 m wall in a day.
Let, the number of men required to build a wall of 26m in one day be x.
Now find the number of men required to build 1 m long wall,
$\dfrac{{15}}{{16.25}}$
Then, the number of men required to build a 26 m long wall is,
$x = 26 \times \dfrac{{15}}{{16.25}}$
Cancel out the common factors from the numerator and denominator from both sides of the equation,
$x = 2 \times 12$
Multiply the terms on the right side to get the result,
$x = 24$
Hence, the number of men required to build a wall of 26m in one day is 24.