Answer:

The investment of 'A' is Rs. 800.

Step-by-step explanation:

Let's denote the investment of 'A' as x and the investment of 'B' as x + 160.

The profit share of a partner is directly proportional to both the amount invested and the time the investment is made. The equation for profit share (P) can be expressed as:

[tex]\[ P \propto \text{Investment} \times \text{Time} \][/tex]

So, the profit share for 'A' [tex](P_A)[/tex] is given by [tex]P_A = x \times 18[/tex] and for 'B' [tex](P_B)[/tex] it is [tex]P_B = (x + 160) \times 24.[/tex]

Now, the problem states that the profit share of 'B' is 60% more than that of 'A':

[tex]\[ P_B = P_A + 0.60 \times P_A \][/tex]

Substitute the expressions for

[tex]P_A \: and \: P_B:[/tex]

[tex]\[ (x + 160) \times 24 = x \times 18 + 0.60 \times (x \times 18) \][/tex]

Expand and simplify both sides:

[tex]\[ 24x + 3840 = 18x + 0.60 \times 18x \][/tex]

Combine like terms:

[tex]\[ 24x + 3840 = 18x + 10.8x \][/tex]

[tex]\[ 24x + 3840 = 28.8x \][/tex]

Subtract 24x from both sides:

[tex]\[ 3840 = 4.8x \][/tex]

Divide by 4.8 to solve for x:

[tex]\[ x = \frac{3840}{4.8} \][/tex]

x = 800

So, the investment of 'A' (x) is Rs. 800.

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