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Amita invested some part of ₹ 35000 at 4% and the rest at 5% interest for one year. Altogether her gain was ₹ 1530. Find out the amounts she had invested at the two different rates. Write your answer in words.

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Let the amount invested at the rate of 4% and 5% be ₹ x and ₹ y respectively.

 According to the first condition, total amount invested = ₹ 35000 

∴ x + y = 35000 …(i)

 According to the second condition,

 total interest received at 4% and 5% is ₹ 1530.

∴ 4 % of x + 5 % of y = 1530 

\(\frac{4}{100}\) x x + \(\frac{4}{100}\) x y = 1530 

∴ 4x + 5y = 153000 …(ii) 

Multiplying equation (i) by 4, we get 

4x + 4y = 140000 …(iii) 

Subtracting equation (iii) from (ii),

Substituting y = 13000 in equation (i), 

x + 13000 = 35000 

∴ x = 35000 – 13000 = 22000

∴ Amita invested ₹ 22000 at the rate of 4% and ₹ 13000 at the rate of 5%.

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