Divide Rs. 6305 into there parts in such a way that at the rate of compound interest of 5% per annum the amount of 1st part in 2 years, the amounts of 2nd part in 3 years and the amounts of 3rd part in 4 years are all equal.

Explanation

Let the three parts be Rs.x, Rs.y and Rs.z respectively.
`:.x+y+z=6305…………………….`1
At the rate of 5% compound interest per annum.
The amountof Rs.x in 2 years `=Rs.(1+5/100)^(2)=Rs.x xx(21/20)^(2)`
The amount of Rs.y in 3 years `=Rs.y(1+5/100)^(3)=Rs.yxx(21/20)^(3)`
The amount of Rs.z is 4 years `=Rs.z(1+5/100)^(4)=Rs.xx(21/20)^(4)`
As per question `x xx(21/20)^(2)=yxx(21/20)^(3)=zxx(21/20)^(4)=k`(let)
`:.x xx(21/20)=kimpliesx=kxx(20/21)^(2)=(400k)/441`
`yxx(21/20)^(3)=kimpliesy=kxx(20/21)^(3)=(8000k)/9261`
`zxx(21/20)^(4)=kimpliesz=kxx(20/21)^(4)=(160000k)/194481`
Then from 1 we get `=(400k)/441+(8000k)/9261+(160000k)/194481=6305`
`implieskxx400/441(1+20/21+400/441)=6305`
`implies(kxx400)/441xx1261/441=6305`
`impliesk=(6305xx441xx441)/(400xx1261)=(441xx441)/80`
`:.x=400/441xx(441xx441)/80=2205`
`y=8000/9261xx(441xx441)/80=2100`
`z=16000/194481xx(441xx441)/80=2000`
`:.` The required three parts of Rs. 6305 ar eRs. 2205, Rs. 2100, Rs. 2000