Question 1197028

An amount of Rs 10000 is put in three investments at the rate of 10% 12% 15% per annum. the combined income is Rs 1310 and combined income  of first and secpnd investment is 190 less of the income from third . find each,s investment
<pre>Let amount invested in first (10%), second (12%) and third (15%) funds be F, S and T, respectively
                                        Then: F + S + T = 10,000 -- eq (i)
                                      .1F + .12S + .15T = 1,310 --- eq (ii)
                                             .1F + .12S = .15T - 190
                                      .1F + .12S - .15T = - 190 --- eq (iii)

                                      .1F + .12S + .15T = 1,310 -- eq (ii)
                                      .1F + .12S - .15T = - 190 -- eq (iii)
                                                    .3T = 1,500 -- Subtracting eq (iii) from eq (ii)
<font color = red><font size = 4><b>Amount invested in the third (15%) fund</font></font></b>, or {{{highlight_green(matrix(1,7, T, "=", "1,500"/.3, "=", "15,000"/3, "=", highlight("$5,000")))}}} 
 
                                      .1F + .12S + .15T = 1,310 --- eq (ii)
                                      .1F + .12S - .15T = - 190 --- eq (iii)         
                                             .2F + .24S = 1,120 ---- Adding eqs (iii) & (ii)
                                           .2(F + 1.2S) = .2(5,600)
                                               F + 1.2S = 5,600
                                                      F = 5,600 - 1.2S --- eq (iv)
                             
                               5,600 - 1.2S + S + 5,000 = 10,000 --- Substituting 5,000 for T and 5,600 - 1.2S for F in eq (i)
                                         - .2S + 10,600 = 10,000
                                                  - .2S = 10,000 - 10,600
                                                  - .2S = - 600
<font color = red><font size = 4><b>Amount invested in the second (12%) fund</font></font></b>, or {{{highlight_green(matrix(1,7, S, "=", (- 600)/(- .2), "=", ("- 6,000")/(- 2), "=", highlight("$3,000")))}}} 
 
                                                       F = 5,600 - 1.2(3,000) ----- Substituting 3,000 for S in eq (iv)
  <font color = red><font size = 4><b>Amount invested in the first (10%) fund</font></font></b>, or F = 5,600 - 3,600 = <font color = red><font size = 4><b>$2,000</font></font></b></pre>