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A,B and C enter into partnership by making investments in the ratio 3: 5: 7. After a year, C invests another Tk. 337600 while a withdraws Tk. 45600 . The ratio of investments then changes to 24:59:67. How much doses A invest initially?

Tk. 140600

Tk. 141600

Tk.131600

Tk. 140500

ANSWER : 2

Descrption

Let's assume that initially, A invested 3x, B invested 5x, and C invested 7x.After a year, C invests an additional Tk. 337600, so C's new investment becomes 7x + 337600.A withdraws Tk. 45600 from the partnership, so A's new investment becomes 3x - 45600.Now, the ratio of investments is given as 24:59:67.According to the given ratios, we can set up the following equations:For the new investment ratios: (3x - 45600) : 5x : (7x + 337600) = 24 : 59 : 67Now, let's simplify the ratios. We can do this by dividing all parts of the ratio by their respective greatest common divisor (GCD):(3x - 45600) / GCD : 5x / GCD : (7x + 337600) / GCD = 24 / GCD : 59 / GCD : 67 / GCDThe simplified ratio is: (3x - 45600) : 5x : (7x + 337600) = 24 : 59 : 67Now, we have three equations based on the ratios of the investments:<ol><li>(3x - 45600) / 24 = 5x / 59</li><li>(3x - 45600) / 24 = (7x + 337600) / 67</li></ol>Let's solve these equations:From equation 1: (3x - 45600) / 24 = 5x / 59Cross-multiply: 59(3x - 45600) = 24 * 5xSimplify: 177x - 2678400 = 120xSubtract 120x from both sides: 57x = 2678400Divide by 57: x = 2678400 / 57 x = 47040Now that we have the value of x, we can find the initial investment of A, which is 3x:Initial investment of A = 3x = 3 * 47040 = 141600So, A initially invested Tk. 141600.

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