Divide 2379 into 3 parts so that their amounts after 2, 3 and 4 years respectively may be equal, the rate of interest being 5% per annum at simple interest. The first part is:
Pick one
A) 759	B) 792	C) 818	D) 828	E) None of these
Let the parts be x, y and [2379 – (x + y)].   x + (x × 2 × 5⁄100) = y + (y × 3 × 5⁄100)   = z + (z × 4 × 5⁄100)   ⇒ 11x⁄10 = 23y⁄20 = 6z⁄5 = k ⇒ x = 10k⁄11, y = 20k⁄23, z = 5k⁄6   But x + y + z = 2379.   ⇒ 10k⁄11 + 20k⁄23 + 5k⁄6 = 2379   ⇒ 1380 k + 1320 k + 1256 k = 2379 × 11 × 23 × 6   ⇒ k = 2379×11×23×6/3965=3×11×23×6/5   ∴ x = (10/11×3×11×23×6/5)=828   Hence, the first part is 828.   Answer 828
<result>D</result>
Divide 2379 into 3 parts so that their amounts after 2, 3 and 4 years respectively may be equal, the rate of interest being 5% per annum at simple interest. The first part is: