Question

The present age of Aman and Naman are in the ratio 4:5 . Eight years hence ,the ratio of their ages will be 5:6. Find their present ages.

Answer 1

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Answer 2

Answer:

The present age of aman and naman is 32 and 40 respectively.

Step-by-step explanation:

• let the present age of Aman is x
• The present age of Naman is y

• Ratio of the ages is given as 4:5. This can be represented as

       $\frac{x}{y} =\frac{4}{5} \\x=\frac{4y}{5}$

After 8 years:

• Age of Aman is $x+8$
• Age of Naman is $y+8$
• The ratio of the ages is $\frac{5}{6}$. This can be represented as

       $\frac{x+8}{y+8} =\frac{5}{6} \\\\6x+48=5y+40\\6x-5y=-8$

• Put value of x in the above equation,

       $6(\frac{4y}{5} )-5y=-8\\24y-25y=-40\\-y=-40\\y=40$

• The value of x is $32$

Conclusion:

The present age of aman and naman is 32 and 40 respectively.