Question

divide 286 into four parts such that the first part increased by 1,the second decreased by 2 the third multiplied by 3 and the fourth divided by 4 will give same result in each case.

Answer 1

let the 4 parts be a,b,c and d respectively.
a+b+c+d=286

a + 1 = k  ⇒ a = k-1
b - 2 = k   ⇒ b = k+2
3 × c = k  ⇒ c = k/3
d/4 = k     ⇒ d = 4k

a+b+c+d=286
⇒ (k-1) + (k+2) + k/3 + 4k = 286
⇒ k+k+k/3+4k-1+2=286
⇒19k/3 = 285
⇒ k = 285×3/19 = 45

a = 45-1 = 44
b = 45+2 = 47
c = 45/3 = 15
d = 4×45 = 180