Question

The ages of Rita and fit a are in the ratio of 5:7.four years from now their ages will be in the ratio of 3:4.their present ages are

Answer 1

rita/fit = 5/7
5x+4/7x+4=3/4 (4 years form now so, add 4)
4(5x+4)=3(7x+4)(by cross multiplication)
20x+16=21x+12(by opening the brackets)
16-12=21x-20x(by transposing)
4=x
therefore,their present ages are:5*x=5*4=20=rita's age
                                                    7*x=7*4=28=fit's age

Answer 2

Let in present
the age of Rita = 5P years
the age of Rit = 7P years ,

after 4 years /
the age of Rita = (5P +4) years
the age of Rit = (7P + 4) years

A/c to question,
the age of Rita / the age of Rit = 3/4
(5P + 4)/( 7P + 4) = 3/4

4( 5P + 4) = 3( 7P + 4)

20P + 16 = 21P + 12

P = 4 ,
hence, present age of Rita = 5P
= 5 ×4
= 20 years

and present age of Rit = 7P
= 7 × 4
= 28 years