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Question

Present ages of Sita and Geeta are in the ratio 4 : 5. Eight years from now the ratio of their ages will be 5 : 6. Find their present ages. [4 MARKS]


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Solution

Concept: 2 Marks
Application: 2 Marks

Let the present ages of Sita and Geeta be 4x years and 5x years respectively.

After eight years. Sita’s age
=(4x+8) years;

After eight years, Geeta’s age
=(5x+8) years.

Therefore, the ratio of their ages after eight years
=4x+85x+8=56

Cross-multiplication gives
6(4x+8)=5(5x+8)

24x+48=25x+40

24x+4840=25x

24x+8=25x

8=25x24x

8=x

Therefore, Sita’s present age
=4x=4×8=32 years

Geeta’s present age
=5x=5×8=40 years


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