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?

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get 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? from screen.

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?

Click here👆to get an answer to your 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?

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?

Rs. 13000 in scheme A, Rs. 12000 in scheme B

Rs. 12000 in scheme A, Rs. 10000 in scheme B

Rs. 11000 in scheme A, Rs. 10000 in scheme B

Rs. 10000 in scheme A, Rs. 13000 in scheme B

Medium Open in App Solution Verified by Toppr

Correct option is B)

Let amount invested in A be Rs. x and in B be Rs. y.

As per the given statements, 0.08x+0.09y=1860.....(1)

And, 0.09x+0.08y=1880.....(2)

Multiplying equation (1) with 8 we get, 0.64x+0.72y=14880.....(3)

Multiplying equation (2) with 9 we get, 0.81x+0.72y=16920.....(4)

Subtracting equation (3) from (4), we get 0.17x=2040=>x=12000

Substituting x=12000 in the equation (1), we get 0.08(12000)+0.09y=1860⇒y=10000

Hence, amount invested A is Rs. 12000 and in B is Rs. 10000

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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 ₹1860 as annual interest. However, had she interchanged the amount of investments in the two schemes, she would have received ₹20 more as annual interest. How much money did she invest in each scheme ?

Answer:

Let the money invested in scheme A =₹x

and the money invested in scheme B = ₹y

Case I: Susan invested ₹ x at 8% p.a. + Susan invested ₹y at 9% p.a. = 1860

\begin{array}{l} \Rightarrow \frac{x \times 8 \times 1}{100}+\frac{y \times 9 \times 1}{100}=1860 \\ \Rightarrow 8 \mathrm{x}+9 \mathrm{y}=186000 \ldots(\mathrm{i}) \end{array}

⇒ 100 x×8×1 + 100 y×9×1 =1860 ⇒8x+9y=186000…(i)

Case II: Interchanging the amount in schemes A and B, we have

\frac{9 \times x}{100}+\frac{8 \times y}{100}=(1860+20) \\ \Rightarrow 9 \mathrm{x}+8 \mathrm{y}=188000 \ldots \text { (ii) }

100 9×x + 100 8×y =(1860+20) ⇒9x+8y=188000… (ii)

Adding (i) and (ii), we get

⇒ x + y = 22000 …(iii)

On subtracting (i) and (ii), we get x – y = 2000 …(iv)

⇒ x = ₹12000

Now, x + y = 22000 [From (iii)]

⇒ y = 22000 – 12000 ⇒ y = 10,000

Hence, the amount invested in schemes A and B are 12000 and 10,000 respectively.

Question 12 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?

Question 12 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?

Byju's Answer Standard IX Mathematics Compound Interest Question 12 S... Question Question 12

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?

Open in App Solution

Let the amount of investments in schemes. A and B be Rs. x and Rs. y. respectively

Case I interest at the rate of

8 %

per annum on scheme A + interest at the rate of

9 %

percent annum on scheme B = Total amount received

⇒ x × 8 × 1 100 + y × 9 × 1 100 = R s .1860 [ ∴ s i m p l e i n t e r e s t = p r i n c i p l e × r a t e × t i m e 100 ] × 8 x + 9 y = 186000

Case II interest at the rate of

9 %

per annum on scheme A + interest at the rate of

8 %

per annum on scheme B = Rs. 20 more as annual interest

⇒ x × 9 × 1 100 + y × 8 × 1 100 = R s 20 + R s . 1860 ⇒ 9 x 100 + 8 y 100 = 1880 9x + 8y = 188000

On multiplying Eq. (i) by 9 and Eq. (ii) by 8 and then subtracting them, we get

72x + 81y = 9 × 186000 72x + 64y = 8 × 188000 ⇒ 17 y = 100 [ ( 9 × 186 ) − ( 8 × 188 ) ]

= 1000 (1674 – 1504) = 1000

× 170 17y = 170000 ⇒ y = 10000

On putting the value of y in Eq (i), we get

8x + 9 × 10000 = 186000 ⇒ 8x = 186000 – 90000 ⇒ 8x = 96000 ⇒ x = 12000

Hence, she invested Rs. 12000 and Rs. 10000 in two schemes A and B, respectively

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