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Susan 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 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:

Consider the amount of investments in scheme A as ₹ x.

Consider the amount of investment in scheme B as ₹ y.

Simple interest = principal x rate x time/100.

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 x 8 x 1/100 + y x 9 x 1/100 = 1860.

8x + 9y = 186000--------------------(1)

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 x 9 x 1/100 + y x 8 x 1/100 = 20 +1860

9x/100 + 8y/100 =1880

9x + 8y= 188000-----------------------(2)

Solve the linear equations (1) and (2)

Multiplying (1) by 9 and (2) by 8 and then subtracting them, we get,

(72x + 81y) - (72x + 64y) = 9 x 186000 - 8 x 188000

17y = 1000[(9 x 186) - (8 x 188)] = 1000(1674 - 1504) = 1000 x 170

17y = 170000 ⇒ y =10000

Substituting the value of y in(1),we get,

8x + 9 x 10000 = 186000

8x = 186000 - 90000

8x = 96000

x = 12000.

Therefore, she invested ₹ 12000 and ₹ 10000 in two schemes A and B respectively.

✦ Try This: Susan invested a certain amount of money in two schemes A and B, which offer interest at the rate of 7% per annum and 8% per annum, respectively. She received Rs 1850 as annual interest. However, had she interchanged the amount of investments in the two schemes, she would have received Rs 30 more as annual interest. How much money did she invest in each scheme

☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 3

NCERT Exemplar Class 10 Maths Exercise 3.4 Problem 12

Susan 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 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

Summary:

Susan 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 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. She invested ₹ 12000 and ₹ 10000 in two schemes A and B respectively.

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