Ruhi invested a certain amount of money in two schemes

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Q:)  Ruhi invested a certain amount of money in two schemes A and B, which offer interest at the rate of 8% per annum and 9% per annum, respectively. She received ₹ 1860 as annual interest. However, had she interchanged the amount of investments in the two schemes, she would have recieved ₹ 20 more as annual interest. How much money did she invest in each scheme ?

Solution: Let Ruhi invest the money in scheme A = ₹ x

and Let invested amount in scheme B = ₹ y

Interest in scheme A = \frac{x \times 8}{100}

Interest in scheme in B = \frac{y \times 9}{100}

Hence,

\frac{x \times 8}{100}+\frac{y\times 9}{100} = 1860

Multiply by 100

⇒ 8x + 9y = 186000  ——(i)

Agian

Interchanging the amount

\frac{x \times x}{100}+ \frac{x \times 8}{100} = 1860+20

⇒ 9x + 8y = 188000 —– (ii)

Multiply by 9 in eq (i) and 8 in eq(ii) and substracting (i) to (ii)

(72x + 81y) – (72x + 64y) = 1,674,000 – 1,504,000

⇒ 72x + 81y – 72x – 64y = 170,000

⇒ 17 y = 170,000

⇒ y = 10,000

Putting the value of y in (i)

8x + 9y = 186000

⇒ 8x + 9×10,000 = 186000

⇒ 8x = 186000 – 90000

⇒ 8x = 96,000

⇒ x = 12,000

Invested amount in scheme A =  ₹12,000

Invested amount in scheme B = ₹ 10,000

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