Question

an amount of rupees 65000 is invested in three bonds at the rates of 6% ,8% and 10% per annum.The total annual income is rupees 4800. The income from the third bond is rupees 600 more than from the second bond . Determine the price of each bond

Answer 1

Answer:

Investment =  Rs. 36154, Rs. 12692, Rs. 16154

Step-by-step explanation:

Amount Invested = Rs. 65000 in bonds of 6% 8% and 10% p.a.

Total Income = Rs. 4800

Income from third bond (I3) = 600 + Income from second bond (I2)

Income from first bond (I1) =  6% of x = 0.06x

Income from second bond (I2) = 8% of y = 0.08y

Income from third bond (I3) = 10% of z = 0.1z

I1+I2+I3 = 4800 and

x+y+z=65000 ------>1

Difference in incomes from third and second = 600

Therefore,

10z/100 - 8y/100 = 600

We get an equation, 10z -8y = 60000 -----> 2

6x/100 + 8y/100 +10z/100 = 4800 (Total income)

Therefore we get, 6x + 8y +10z = 480000 ----->3

Now we have 3 equations and 3 unknowns, hence it is possible to solve them,

On solving, we get,  x = Rs. 36154, y= Rs. 12692, z =  Rs. 16154.

Answer 2

Answer:

Step-by-step explanation:

Amount Invested = Rs 65000

Bond 1  = Rs  1000 A

Bond 2 = Rs  1000 B

Bond 3 = 65000 - 1000A - 1000B =  1000(65 - A -B) Rs

Income from Bond 1 = (6/100)* 1000A = 60A Rs

income from Bond 2 = (8/100) * 1000B = 80B  Rs

Income from bond 3 = (10/100) * 1000(65-A-B) = 100(65 - A - B)  Rs

60A + 80B + 100(65 - A - B) = 4800

=> 40A + 20B = 1700

=> 2A + B = 85  - Eq 1

100(65-A-B) = 600 + 80B

=> 100A + 180B = 5900

=> 5A + 9B = 295   - Eq 2

9 * Eq1 - Eq2

13A = 470

=> A = 470/13

2(470/13) + B = 85

=> B = 165/13

First Bond = 1000A =  470000/13  =  Rs 36153.85

Second Bond = 1000B = 165000/13 = Rs 12692.30

Thiird bond = 1000( 65 - 470/13 - 165/13) = 210000/13 =  Rs 16153.85