Question

6400 workers were employed to construct a river bridge in four years. At the end of
the first-year, 25% workers were retrenched. At the end of the second year, 25% of
those working at that time were retrenched. However, to complete the project in
time, the number of workers was increased by 25% at the end of the third year. How
many workers were working during the fourth year?​

Answer 1

Answer:

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Answer 2

Question:

6400 workers were employed to construct a river bridge in four years. At the end of the first-year, 25% workers were retrenched. At the end of the second year, 25% of those working at that time were retrenched. However, to complete the project in time, the number of workers was increased by 25% at the end of the third year. How many workers were working during the fourth year?​

Answer:

There will be 4500 workers during the 4th year.

Given:

Total number of workers = 6400

The rate of workers retrenched after 1 year = 25%

The rate of workers retrenched after the 2nd year = 25%

To find:

The number of workers at the fourth year.

Explanation:

Case-1:

Since in the 1st and 2nd years the number of workers retrenched in the same rate. So, the number of workers at the bigining of the 3rd year can be calculated by the method of depreciating rate.

Let's assume,

P = 6400

R= 25%

n = 2 years.

∴ The number of workers at the begining of the third year_

$P(1-\frac{R}{100} )^{n}$

$= 6400(1-\frac{25}{100} )^{2}$

$= 6400(\frac{100-25}{100} )^{2}$ [∵ The L.C.M. of the denominators is 100]

$=6400(\frac{75}{100} )^{2}$

$= 6400(\frac{3}{4})^{2}$ [∵ Dividing 75 and 100 by 25.]

$= 6400(\frac{9}{16})$

$=(\frac{6400×9}{16})$

=(400×9) [∵Dividing 6400 by 16 and the denominator gets canceled.]

= 3600 workers.

∴ At the begining of the 3rd year there were 3600 workers.

Case-2:

Number of workers = 3600.

Increased rate = 25%.

∴ The number of workers were increased at the end of the 3rd year_

3600×(25/100)

= (3600/4) [∵ Dividing 25 and 100 by 25.]

= 900 workers.

∴ The number of workers at the 4th year _

(3600+900) workers.

= 4500 workers.

∴ There will 4500 workers at the 4th year.