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_{0 }[1+ r/100]^{n}

where r% is the rate of growth, n is the number of years, V_{0} 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 = V0 [ 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.**