[16] A year ago the proportion between Sham and Amirs age was 4:3. 1 year hence the proportion of their a

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A year ago the proportion between Sham and Amirs age was 4:3. 1 year hence the proportion of their ages will be 5:4. The total of their current ages is :

Explanation:
Let the present age of Sham be X.
Let the present age of Amir be Y.
=> Age of Sham one year back = X-1.
=> Age of Amir one year back = Y-1.
And, Age of Sham after one year = X+1.
And, Age of Amir after one year = Y+1.
Ratio of Sham's and Amir's ages one year back = 4:3.
=> X-1/Y-1 = 4/3
3X-3 = 4Y-4
3X-4Y= -1 -------------> 1
Ratio of Sham's and Amir's ages after one year = 5:4.
=> X+1/Y+1 = 5/4
4X+4 = 5Y+5
4X-5Y = 1 -----------------> 2
Solving 1 and 2, we get
X=9 and Y=7.
The sum of their ages is 16

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