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?

Answer 1

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.