This year the number of blood donners in a hospital is 24000. If the number of blood donners increases by 5% in every 6 months, then in how much time will the number of blood donners be 27783?

Explanation

This year the number of blood donners is 24000. The number of blood donners increases by 5% in every 6 months, i.e. 10% in every year. Let the required time be `t` years to reach the number of blood donners form 24000 to 27783.
As per question `24000xx(1+(10/2)/100)^(2t)=27783`
`implies24000xx(1+1/20)^(2t)=27783`
`implies((20+1)/20)^(2t)=27783/24000`
`implies(21/20)^(2t)=27783/24000=9261/8000=(21/20)^(3)`
`implies(21/20)^(2t)=(21/20)^(3)implies2t=3impliest=3/2=1 1/2`
Hence after `1 1/2` years the number of blood donners will be 27783.