Question

May the present age of Latha and Uma be 3x and 4x and 10 years back, Latha was half of Uma's age. If the ratio of their present is 3:4, What will be the total of their present age ?

Answer 1

Given: Present age of Latha = 3x

           Present age of Uma = 4x

          10 years ago, age of Latha = 1/2*age of Uma

           Ratio of their present ages = 3:4

To find: Total of Latha and Uma's present ages

Solution:

According to the given question,

10 years ago, Age of Latha was 1/2 of Uma's age

Hence, If present age of Latha is 3x, it would have been 3x - 10 ten years ago which is also equal to half of Uma's age:-

i.e.,     3x - 10 = $\frac{1}{2}$ × 4x

Simplifying the above equation,

          3x - 10 = 2x

          3x - 2x = 10

                   x = 10

Hence, present age of Latha (3x) = 3 × 10 = 30 years

Present age of Uma (4x) = 4 × 10 = 40 years

Total of their present ages = 3x + 4x

                                              = 30 + 40

                                              = 70 years