Question

A person has rupees 35000 that he has divided into three invests, part of the money is invested in a saving account with annual rate of interest of 6%, paath ine 7% annual yield Bond and the remainder in a business in 2006 when he lost 6% of the money that he invested in that business, his net income from all three investments was rupees 660. If he invested Rs 3000 more in the business then in saving account how much was invested in each?

Answer 1

Given : A person has rupees 35000 that he has divided into three invests, part of the money is invested in a saving account with annual rate of interest of 6% , 7% annual yield Bond , lost 6% of the money that he invested in that business

To find :  how much was invested in each

Solution:

Let say Amount invested are

1000x , 1000y & 1000z at  6 % , 7 %   & - 6 %  

1000x + 1000y + 1000z = 35000

=> x + y + z  = 35

1000x *6/100  + 1000y*7/100  + 1000z(-6/100) = 660

=>  6x + 7y - 6z  = 66

=> 6(x - z) + 7y = 66

1000z = 1000x + 3000

=> z = x +  3

=>  x - z = - 3

6(x - z) + 7y = 66

=> 6(-3) + 7y = 66

=> 7y = 84

=> y = 12

x + y + z  = 35  => x + y + x + 3  = 35 => 2x + y = 32

2x + 12 = 32

=> 2x = 20

=> x = 10

z = 13

10000 , 12000 , 13000

Rs 10000 invested in  Saving account

Rs 12000 invested in Bond

Rs 13000 invested  in Business

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Answer 2

Given:

Total money invested = Rs. 35000

Interest rate of savings account = 6%

Interest rate of annual yield bond = 7%

Interest rate of business = 6%

Formula for Simple Interest is as follows:

$SI = \dfrac{PRT}{100}$

Where P is the money invested

R is the rate of interest and

T is the Time for which the money is invested.

Let amount invested in Savings account = $x$ Rs

So, Amount invested in Business = $(x+3000)$ Rs

Amount left, which is invested in Annual Yield bond = $(35000-(x+3000)-x) = (32000-2x)\ Rs$

As per question statement, there are profits from Savings and Annual yield bond and there is loss of 6% from Business, so interest will be negative in case of business.

Writing equation:

$\dfrac{x \times 6 \times 1}{100} + \dfrac{(32000-2x) \times 7 \times 1}{100} - \dfrac{(3000+x) \times 6 \times 1}{100} =660\\\Rightarrow \dfrac{6x}{100} + \dfrac{(32000\times 7-14x) }{100} - \dfrac{8000}{100}-\dfrac{6x}{100}}=660\\\Rightarrow \dfrac{(32000\times 7-14x) }{100} - 180=660\\\Rightarrow \dfrac{(32000\times 7-14x) }{100} =840\\\Rightarrow 224000-14x =84000\\\Rightarrow 224000-84000 =14x\\\Rightarrow 14x = 140000\\\Rightarrow x = 10000\ Rs$

Money invested in Savings account, x = 10000 Rs

Money invested in annual yield bond = 32000 -  2x = 32000- 20000 = 12000 Rs

Money invested in Business, x+3000 = 13000 Rs