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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. |
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Answer» 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. |
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