Question

- An agent of an insurance company discuss a
money back policy with Mr. X. If a person
invested some amount at the rate of 15%
simple interest and some other amount at
the rate of 17% simple interest. He received
yearly interest of 190. But if he had
interchanged amount invested, he would
have received 4 more as interest.
How much amount did he invest at different
rates?​

Answer 1

Answer:

Rs 700 at 15% and Rs 500 at 17% interest

Step-by-step explanation:

As we Know, Simple Interest = $\frac{P*R*T}{100}$ Here, P = Principal

                                                                        R = Rate of interest

                                                                        T = Time

According to the question, the sum of interest generated at 15% and 17% rates is Rs 190. So, let the principal at 15% be x , the principal at 17% be y and time be 1 year.

So, equation (1) will become,

$\frac{x*15*1}{100}$+ $\frac{y*17*1}{100}$= 190

$x=\frac{190-0.17y}{0.15}$

Similarly, after exchanging the principal the equation become as shown below:

$\frac{x*17*1}{100}$+ $\frac{y*15*1}{100}$= 194

On putting the value of x we get,

$0.17(\frac{190-0.17y}{0.15} )+0.15y=194\\32.3-0.0289y+0.0225y=29.1\\y=500$

Similarly, put the value of y in the expression of x as shown below:

$x=\frac{190-(0.17*500)}{0.15} \\ =700$

Answer 2

Answer:

The amount invested at 15% simple interest  Rs 700

The amount invested at 17% simple interest  Rs 500

Step-by-step explanation:

Given as :

Let The amount invested at 15% simple interest = Rs x

Let The amount invested at 17% simple interest = Rs y

Total interest earn in 1 year = S.I = 190

∵ Sample Interest = $\dfrac{principal\times rate\times time}{100}$

Total interest = $\dfrac{x\times 15\times 1}{100}$ + $\dfrac{y\times 17\times 1}{100}$

Or, 190 = $\dfrac{x\times 15\times 1}{100}$ + $\dfrac{y\times 17\times 1}{100}$

Or, 190 × 100 = 15 x + 17 y

or, 15 x + 17 y = 19000                  ............A

Again

The amount invested at 17% simple interest = Rs x

Again The amount invested at 15% simple interest = Rs y

Total interest earn in 1 year has received 4 more than earlier Interest = s.i 190 + 4 = 194

∵ Sample Interest = $\dfrac{principal\times rate\times time}{100}$

Or, 194 = $\dfrac{y\times 15\times 1}{100}$  + $\dfrac{x\times 17\times 1}{100}$

Or, 194 × 100 = 15 y + 17 x

or, 15 y  + 17 x = 19400                  ...........B

Solving eq A and eq B

17 (17 x + 15 y) - 15 (15 x + 17 y) = 17 ×  19400 - 15 × 19000

Or, 289 x + 255 y - 225 x - 255 y = 329800 - 285000

Or, 64 x + 0 = 44800

∴  x = $\dfrac{44800}{64}$

i.e  x = 700

So, The amount invested at 15% simple interest =  x = Rs 700

Put the value of x in eq B

15 y  + 17 x = 19400

or, 15 y  + 17 × 700 = 19400

Or, 15 y = 19400 - 11900

Or, 15 y = 7500

∴     y = $\dfrac{7500}{15}$

i.e  y = Rs 500

So, The amount invested at 17% simple interest = y = Rs 500

Hence, The amount invested at 15% simple interest  Rs 700

And The amount invested at 17% simple interest  Rs 500   Answer