# 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.

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by Tirkey

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by Tirkey

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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

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