The present ages of Rafi and fathima are in the ratio 7:5. Ten years later the ratio of their ages will be 9:7. Find their present ages step by step.
Answers
Since the present ratio of ages of Rafi and Fathima is 7:5.
We may take, Rafi's age to be 7x and the Fathima's age to be 5x
(Note that ratio of 7x and 5x is 7x:5x and which is same as 7:5)
After 10 years Rafi's age =7x+10
And Fathima's age =5x+!0
After 10 years, the ratio of Rafi's age and Fathima's age is 7x+10:5x+10
But according to the given data this ratio is equal to 9:7
⇒ 7x+10:5x+10=9:7
ie., 7(7x+10)=9(5x+10)
⇒ 49x+70=45x+90
Did you notice that in the above equation we have algebraic expressions on both sides.
Note let us learn how to solve such equations.
The above equation is 49x+70=45x+90
⇒ 49x−45x=90−70 (Transposing 70 to RHS and 45 to LHS)
∴ 4x=20
∴ x= 20/4 = 5
Therefore Rafi's age =7x = 7×5 = 35 years.
And Fathima's age =5x = 5×25 years.
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