Let’s assume that Y gets a share of ₹y and Z gets a share of ₹z.

Given that X gets three-fifths of what Y gets, we can write the equation:

X = (3/5)Y

We also know that the ratio of Y’s share to Z’s share is 6:11, so we can write another equation:

Y/Z = 6/11

Now, let’s solve these equations to find the values of X, Y, and Z.

From the first equation, we can rewrite it as:

Y = (5/3)X

Substituting this value of Y in the second equation, we get:

(5/3)X/Z = 6/11

Cross-multiplying, we have:

11(5/3)X = 6Z

Simplifying, we get:

55X = 18Z

Now, we know that the sum of X, Y, and Z’s shares is ₹2060. So we can write another equation:

X + Y + Z = 2060

Substituting the values of X and Y from the previous equations, we have:

X + (5/3)X + Z = 2060

Simplifying, we get:

(8/3)X + Z = 2060

Now, let’s solve these equations simultaneously.

From the equation 55X = 18Z, we can write:

X = (18/55)Z

Substituting this value of X in the equation (8/3)X + Z = 2060, we have:

(8/3)(18/55)Z + Z = 2060

Simplifying, we get:

(144/165)Z + Z = 2060

(144Z + 165Z)/165 = 2060

309Z/165 = 2060

309Z = 2060 * 165

Z = (2060 * 165)/309

Z ≈ ₹1100

Now, substituting this value of Z in the equation X = (18/55)Z, we have:

X = (18/55) * 1100

X ≈ ₹360

Finally, we can find Y by substituting the values of X and Z in the equation X + Y + Z = 2060:

360 + Y + 1100 = 2060

Y = 2060 - 360 - 1100

Y ≈ ₹600

Therefore, the shares of X, Y, and Z are approximately ₹360, ₹600, and ₹1100, respectively.