A sum ₹ 1440 is lent out in three parts in such a way that the interest on first part at 2% for 3 yr, second part at 3% for 4 yr and third part at 4% for 5 yr equal . Then, the difference between the largest and the smallest sum is?

Let the first part be ₹ A.
second part be ₹ B
and third part be Rs C
According to the question.
(A x 2 x 3)/100 = (B x 3 x 4)/100 = (C x 4 x 5)/ 100
⇒ 3A = 6B = 10C = k
∴ A = k/3, B = k/100 and C = k /10
Now, A + B + C = 1440
⇒ k/3 + k/6 + k/10 = 1440 ⇒ k = 2400
∴ so the difference = k/3 - k/10 = 7k/30 = 7/30 x 2400 = ₹ 560