An amount of Rs 5000 is put into three investments at the rate of interest of 6+, 7+ and 8+ per annum. The total annual income is Rs. 358. If the combined income from the first two investments is Rs. 70 more than the income from third, find the amount of each investment by matrix method.

Let x = 6% amt (1st investment) Let y = 7% amt (2nd investment) Let z = 8% amt (3rd investment) The total invested equation: x + y + z = 5000 : The total annual income equation: =>06x + .07y + .08z = 358 It says,"The income from the first two investments is Rs.70 more than the income from the third investment." equation for this: =>06x + .07y = .08z + 70 =>06x + .07y - .08z = 70 Use elimination by subtracting the above equation from the total income equation =>06x + .07y + .08z = 358 =>06x + .07y - .08z = 70 ------------------------- subtraction eliminates x and y 0x + 0y + .16z = 268 z = 288%2F.16 z = Rs.1800 invested at 8% Using the total equation; z = 1800 =>x + y + 1800 = 5000 =>x + y = 5000 - 1800 =>x + y = 3200 y = (3200-x); use for substitution : Using the total income equation: z = 1800 =>06x + .07y + .08(1800) =>06x + .07y + 144 = 358 =>06x + .07y = 358 - 144 =>06x + .07y = 214 Substitute (3200-x) for y, find x .06x + .07(3200-x) = 214 .06x + 224 - .07x = 214 .06x -.07x = 214 - 224 -.01x = -10 x = %28-10%29%2F%28-.01%29 x = Rs.1000 amt invested at 6% Try to find Y the same way. Hope this helped you!