# 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?

### Mohammed

Guys, does anyone know the answer?

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?

**A**

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

**B**

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

**C**

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

**D**

## 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

Was this answer helpful?

491 45

## Susan invested certain amount of money in two schemes A and B which offer interest at the rate of 8 ...

Free solutions for Mathematics Exemplar Problems - class 10 Chapter 4 - Pair of Linear Equations in Two Variables Pair of Linear Equations in Two Variables - Exercise 3.4 question 11. These explanations are written by Lido teacher so that you easily understand even the most difficult concepts

## NCERT Exemplar Solutions Class 10 Mathematics Solutions for Pair of Linear Equations in Two Variables - Exercise 3.4 in Chapter 3 - Pair of Linear Equations in Two Variables

Prev Question 11 Next

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.

Related Questions

**Graphically, solve the following pair of equations:****2_x_** **+** **_y_** **= 6****2_x_** **–** ...

**Determine, graphically, the vertices of the triangle formed by the lines _y_** **=** **_x_, 3_y_**...

**Find the area of the quadrilateral and graph formed by the lines and the** **_x_–axis of equations...

**The cost of 4 pens and 4 pencil boxes is Rs 100. Three times the cost of a pen is Rs 15 more than ...

**Determine, algebraically, the vertices of the triangle formed by the lines****3_x_** **–** **_y_**...

A person, rowing at the rate of 5 km/h in still water, takes thrice as much time in going 40 km upst...

Was This helpful?

## 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

Suggest Corrections 42

SIMILAR QUESTIONS

**Q.**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?

**Q.**

Karan invested money in two schemes A and B offering compound interest at 8% per annum compounded annually and 9% per annum compounded annually. If the total amount of interest accrued through two schemes together in two years was Rs.4818.30 and the total amount invested was Rs.27,000, what was the amount invested in Scheme A?

**Q.**Sandeep invested Rs. 2500 in a scheme offering 20% per annum simple interest. Had he invested the same amount in another scheme offering 25% simple interest for two more years than the first scheme, he would have received Rs. 1500 more interest. Find the time period of investment in the second scheme.

**Q.**A man invested an amount at 10% per annum and another amount at 8% per annum simple interest. Thus, he received ₹1,350 as annual interest. Had he interchanged the amounts invested, he would have received ₹45 less as interest. What amounts did he invest at different rates?

**Q.**

Babita invested a sum of money for 2 years at 4% per annum simple interest and earned Rs.480 as the interest.

How much more amount would she get if she had invested the same sum for the same time at the same rate compounded annually?

RELATED VIDEOS

Simple and Compound Interest

MATHEMATICS Watch in App EXPLORE MORE Compound Interest

Standard IX Mathematics

Guys, does anyone know the answer?