# 20,000 Football player were registered with Manchester United Football camp. The number of players increased at the rate of 8% every six months. Find

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20,000 Football player were registered with Manchester United Football camp. The number of players increased at the rate of 8% every six months. Find the time period at the end of which the total number of Football players becomes 23328.
1. 2 years
2. 1.5 years
3. 1 year
4. None of theses

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Correct Answer - Option 3 : 1 year

Given

No. of Football Player were registered = 20,000

Rate = 8% for every six months

Total number of players to be = 23,328

Formula Used

V = V[1+ r/100]n

where r% is the rate of growth, n is the number of years, V0 is the present measure of the quantity and V is the measure of the quantity after few years.

Calculation

Here, rate of increase of the number of players per unit time (six months) = 8%. Let the number of units of time (six months) be n.

Using, V = V[ 1+ r/100]n , we get

⇒ 23,328 = 20,000 (1 + 8/100)n = 20,000 (108/100)n

⇒ 23328/20000 = (108/100)n

⇒ (729/625) = (108/100)n

⇒ (27/25)2= (27/25)n

⇒ n= 2

So, The time period = 2 × (six months) = 12 months = 1 year

∴ In 1 year, The total number of players becomes 23,328.