This question is taken from linear equations in two variables in which we have to calculate the invested amount if the total interest received is 1350 from two different interest rates 8% and 10%.
Kindly solve the above problem
RS Aggarwal, class 10, chapter 3E, question no 28
Let the amounts invested at 10% and 8% be Rs.x and Rs.y respectively.
Then as per the question
x × 10 × 1/ 100 = y × 8 × 1/ 100 = 1350
10x + 8y = 135000 …………..(i)
After the amounts interchanged but the rate being the same, we have
x × 8 × 1/ 100 = y × 10 × 1/ 100 = 1350 – 45
8x + 10y = 130500 …………….(ii) Adding (i) and (ii) and dividing by 9, we get
2x + 2y = 29500 ……………(iii) Subtracting (ii) from (i), we get
2x – 2y = 4500
Now, adding (iii) and (iv), we have 4x = 34000
x = 34000/4 = 8500
Putting x = 8500 in (iii), we get
2 × 8500 + 2y = 29500
2y = 29500 – 17000 = 12500
y = 12500/2 = 6250
Hence, the amounts invested are Rs. 8,500 at 10% and Rs. 6,250 at 8%.