A sum of ` 1440 is lent out in three parts in such a way that the interests on first part at 2% for 3 years, second part at 3% for 4 years and third part at 4% for 5 years are equal. Then the difference between the largest and the smallest sum is
(a)` 200
(b)` 400
(c)` 460
(d)` 560
Answer
Answer (as printed): D
Explanation
Let the parts be ` x, ` y and ` [1440 – (x + y)]. Then, x × 2 × 3 y × 3 × 4 [1440 − ( x + y )] × 4 × 5 = = 100 100 100 \ 6x = 12y or x = 2y. x × 2 × 3 [1440 – ( x + y )] × 4 × 5 = So, 100 100 ⇒ 12y = (1440 – 3y) × 20 ⇒ 72y = 28800 ⇒ y = 400. First part = x = 2y = ` 800, Second part = ` 400, Third part = ` [1440 – (800 + 400)] = ` 240. ∴ Required difference = ` (800 – 240) = ` 560.
Explanation as extracted from the printed page; notation may be imperfect.