A sum of Rs.7700 is to be divided among three brothers Zain, Zaid and Zohaib in such a way that simple interest on each part at 5% per annum after 1, 2 and 3 years, respectively remains equal. The share of Zain is more than that of Zohaib by:
To find the share of each brother, we need to divide the sum of Rs.7700 among them.
Let's assume the share of Zain, Zaid, and Zohaib as x, y, and z respectively.
According to the given condition, the simple interest on each share should be equal after 1, 2, and 3 years. Therefore, we can set up the following equations:
1-year interest: x * 0.05 = y * 0.05 = z * 0.05 ------(1)
2-year interest: x * 0.05 * 2 = y * 0.05 * 2 = z * 0.05 * 2 ------(2)
3-year interest: x * 0.05 * 3 = y * 0.05 * 3 = z * 0.05 * 3 ------(3)
From equation (1), we can conclude that x = y = z (as the interest rates are the same).
Now, let's solve equations (2) and (3) to find the relation between x and z.
2-year interest: x * 0.1 = z * 0.1 (as x = y and z = y)
3-year interest: x * 0.15 = z * 0.15 (as x = y and z = y)
Cancelling out the common factors (0.1 and 0.15), we get:
2x = 2.5z ------(4)
3x = 3.5z ------(5)
Multiplying equation (4) by 1.5, we get:
3x = 3z ------(6)
Comparing equations (5) and (6), we can say that:
3x = 3z = 3.5z
This means that the share of Zain (x) is more than that of Zohaib (z) by Rs. 0.5.
So, the share of Zain is more than that of Zohaib by Rs. 0.5.