Soma auntie deposits `6,20,000Rs` in such a way in three banks at the rate of simple interest of `5%` per annum for `2` years , `3` years and `5` years respectively so that the total interests in the `3` banks are equal. Calculate the money deposited by Soma auntie in each of the three banks.

Explanation

Let Soma auntie deposited `Rs x`, `Rs y` and `Rs z` respectively in the `1st`, `2nd`, and `3rd` bank.
As per question, `x+y+z=620000`………`(1)`
The simple interest of `Rs x` in `2` years at the rate of `5%` per annum `=Rs(x xx5xx2)/(100)=Rs(x)/(10)`
At the same rate, simple interest of `Rs y` in `3` years `=Rs(yxx5xx3)/(100)=Rs(3y)/(20)`
Also, at the same rate, simple interest of `Rs z` in `5` years `=Rs(zxx5xx5)/(100)=Rs(z)/(4)`
As per question, `(x)/(10)=(3y)/(20)=(z)/(4)=k` (let)
`implies2x=3y=5z=k` [Multiplying by `20`]
`impliesx=(k)/(2)`, `y=(k)/(3)` and `z=(k)/(5)`
Now, putting these values of `x`, `y`, `z` in `(1)` we get,
`(k)/(2)+(k)/(3)+(k)/(5)=620000`
or, `(15k+10k+6k)/(30)=620000`
or, `31k=620000xx30`
or, `k=(620000xx30)/(31)`
or, `k=20000xx30=600000`
`:.x=(600000)/(2)=300000`
`y=(600000)/(3)=200000`
`z=(600000)/(5)=120000`
`:.` Some auntie deposited `Rs300000`, `Rs200000` and `Rs120000` respectively in these banks.