A sum of ₹1440 is divided into three parts such that the interest earned on the first part at 2% for 3 years equals the interest on the second part at 3% for 4 years, which equals the interest on the third part at 4% for 5 years. Find the difference between the largest and smallest parts.

Question

Accepted Answer

Let the three parts be ₹x, ₹y, and ₹[1440 - (x + y)]. Since the interests on all three parts are equal, we can write:

(x × 2 × 3)/100 = (y × 3 × 4)/100 = [(1440 - (x + y)) × 4 × 5]/100

From the first equality:
6x/100 = 12y/100
6x = 12y
x = 2y

Using this relationship in the second equality:
12y/100 = [(1440 - (2y + y)) × 20]/100
12y/100 = [(1440 - 3y) × 20]/100
12y = (1440 - 3y) × 20
12y = 28800 - 60y
72y = 28800
y = 400

Therefore:
First part = x = 2y = 800
Second part = y = 400
Third part = 1440 - (800 + 400) = 240

The difference between the largest and smallest parts is:
800 - 240 = 560

Answer

Answer

Answer