Problem:
Divide ₹2522 into three parts such that their amount at 5% p.a compound interest in 4, 5, and 6 years respectively may all be equal.

Solution:
Let the three parts be x, y, and z.

Hence, x + y + z = ₹2522

Let the amount at 5% p.a compound interest for 4, 5, and 6 years be A.

Let the principal for each part be P.

Then, A = P(1 + R/100)^T

Where,
R = 5%
T = 4, 5, and 6 years

Hence, P1 = x, P2 = y, and P3 = z

By applying the compound interest formula, we get:

A = P(1 + R/100)^T

A1 = P1(1 + R/100)^4
A2 = P2(1 + R/100)^5
A3 = P3(1 + R/100)^6

As A1 = A2 = A3, we get:

P1(1 + R/100)^4 = P2(1 + R/100)^5 = P3(1 + R/100)^6

Let P1 = a, P2 = b, and P3 = c

Hence, we get:

a(1 + R/100)^4 = b(1 + R/100)^5 = c(1 + R/100)^6

Now, let us assume k = (1 + R/100)

Hence, we get:

a(k)^4 = b(k)^5 = c(k)^6

Let b = ak and c = bk

Hence, we get:

a(k)^4 = ak(k)^5 = ak^2(k)^6

a(k)^4 = ak^6 = ak^8

a = k^4
b = k^6
c = k^8

Now, we can write:

x = ak^4 = k^8
y = bk^6 = k^10
z = ck^8 = k^12

Therefore, x + y + z = k^8 + k^10 + k^12 = k^8(1 + k^2 + k^4)

Also, x + y + z = ₹2522

Hence, we get:

k^8(1 + k^2 + k^4) = ₹2522

On solving this equation, we get:

k^2 = 2

Hence, k = √2

Therefore, we get:

a = k^4 = 2
b = k^6 = 4
c = k^8 = 8

Hence, the three parts are ₹2, ₹4, and ₹8.

Answer: Therefore, the required division of ₹2522 into three parts is ₹2, ₹4, and ₹8, respectively.