Q.A farmer deposited some money in the village post office. After 4 years, he found that the total amount including interest had become ₹434. He calculated that the interest he received was \(\frac{6}{25}\) of his principal amount. Find how much money he had originally deposited and what annual rate of simple interest the post office gave.

Let us assume he deposited ₹\(x\). \(\therefore\) He received interest of \(x \times \cfrac{6}{25} = \cfrac{6x}{25}\) According to the question: \[ x + \cfrac{6x}{25} = 434 \Rightarrow \cfrac{25x + 6x}{25} = 434 \Rightarrow \cfrac{31x}{25} = 434 \Rightarrow x = 434 \times \cfrac{25}{31} = 350 \] \(\therefore\) He deposited ₹350, and the interest over 4 years = ₹434 − ₹350 = ₹84 \(\therefore\) Rate of interest = \(\cfrac{100 \times 84}{350 \times 4}\% = 6\%\) Conclusion: He deposited ₹350, and the post office gave simple interest at an annual rate of 6%.
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