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Question
Susan invested 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 Rs 1860 as annual interest. However, had she interchanged the amount of investments in the two schemes, she would have received Rs 20 more as annual interest. How much money did she invest in each scheme?
Solution
Let the amount of investments in schemes A and B be ₹ x and ₹ y, respectively.
Case I: Interest at the rate of 8% per annum on scheme A + Interest at the rate of 9% per annum on scheme B = ₹ 1860
⇒ `(x xx 8 xx 1)/100 + (y xx 9 xx 1)/100` = 1860 .....`[because "Simple interest" = ("Principal" xx "Rate" xx "Time")/100]`
⇒ 8x + 9y = 186000 ......(i)
Case II: Interest at the rate of 9% per annum on scheme A + Interest at the rate of 8% per annum on scheme B = ₹ 1860 + ₹ 20
⇒ `(x xx 9 xx 1)/100 + (y xx 8 xx 1)/100 = 20 + 1860`
⇒ `(9x)/100 + (8y)/100` = 1800
⇒ 9x + 8y = 188000 ......(ii)
On multiplying equation (i) by 9 and equation (ii) by 8 and then subtracting them, we get
(72x + 81y) – (72x + 64y) = 9 × 186000 – 8 × 188000
⇒ 17y = 1000[(9 × 186) – (8 × 188)]
= 1000(1674 – 1504)
= 1000 × 170
17y = 170000
⇒ y = 10000
On putting the value of y in equation (i), we get
8x + 9 × 10000 = 186000
⇒ 8x = 186000 – 90000
⇒ 8x = 96000
⇒ x = 12000
Hence, she invested ₹ 12000 and ₹ 10000 in two schemes A and B respectively.
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