# Linear Equation 27

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**The ages of A and B are in the ratio of 9 : 4. Seven years hence, the ratio of their ages will be 5 : 3. Find their ages.**

**Solution:** Let the age of A = x years and the age of B = y years

Therefore, x / y = 9 / 4 ; => 4 x - 9 y = 0 ------------------------- (i)

**7 years hence :** A's age will be x + 7 years and B's age will be y + 7 years.

Therefore, (x + 7) / (y + 7) = 5 / 3

=> 3 x + 21 = 5 y + 35

=> 3 x - 5 y = 14 ---------------------------------------------------- (ii)

On solving equation (i) and (ii), we get : x = 18 and y = 8

**Therefore, A's age = 18 years and B's age = 8 years**