Question
Divide 45 into 4 parts such that if the first is
increased by 2, the second is decrease by 2, the third is multiplied by 2 and the fourth divided by 2, the result is the same. Find out First part?Solution
ATQ, Let the four parts be x, y, z, and w. Denote the common result by k. From the conditions: 
Thus, we can express the parts in terms of k:
The sum of the parts is:
Simplifying this gives = 4k + k/2 = 45 Multiply the equation by 2 to get rid of the fraction = 8k+k = 90 Solving for 9k = 90 ⇒ k = 10 Finally, the first part x is = k − 2 = 10−2 = 8 Thus, the first part is 8.
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