Saumya borrowed $₹ 15, 000$ at the rate of $12 %$ p.a. for two years and another amount at the rate of $15 %$ for two years. The total interest paid by her was $₹ 9, 000$ . Find the amount she borrowed at $15 %$ p.a.

₹ 31, 000

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₹ 28, 000

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₹ 33, 000

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₹ 18, 000

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Solution

The correct option is D $₹ 18, 000$
Interest paid for borrowing $₹ 15, 000$ at the rate of $12 %$ p.a. for two years $= \frac{15, 000 \times 12 \times 2}{100} = ₹ 3, 600$

Let $₹ x$ be borrowed for two years at the rate of $15 %$ p.a.
Interest $= \frac{x \times 15 \times 2}{100} = ₹ \frac{3 x}{10}$

The total interest paid $= ₹ 9, 000$
$\Rightarrow ₹ 4500 + ₹ \frac{3 x}{10} = ₹ 9, 000$
$\Rightarrow \frac{3 x}{10} = 9, 000 - 3, 600$
$\Rightarrow \frac{3 x}{10} = 5, 400$
$\Rightarrow \frac{x}{10} = 1, 800$
$\Rightarrow x = 18, 000$

The amount borrowed at $15 %$ p.a. is $₹ 18, 000$ .

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Saumya borrowed ₹15,000 at the rate of 12% p.a. for two years and another amount at the rate of 15% for two years. The total interest paid by her was ₹9,000. Find the amount she borrowed at 15% p.a.

Saumya borrowed $₹ 15, 000$ at the rate of $12 %$ p.a. for two years and another amount at the rate of $15 %$ for two years. The total interest paid by her was $₹ 9, 000$ . Find the amount she borrowed at $15 %$ p.a.