Question

The present age of Rafi and Fathima are in ratio 7 : 5. Ten years later the ratio of their ages is 9 : 7. Find their present age.

Answer 1

Hint: Now we have the ratio of present age of Rafi and Fathima to be 7 : 5. Hence if we take k as constant we can say that the age of Rafi is 7k and the age of Fathima is 5k. Now after 10 years their age is 7k + 10 and 5k + 10 and we are given that this ratio is 9 : 7. Hence cross multiplying the equation we get the value of k. Hence we can substitute the value of k to find their present age.

Complete step-by-step answer:
Now we have that the present age of Rafi and Fathima are in ratio 7 : 5. Now let k be the constant of this ratio.
Then the age of Rafi was 7k and the age of Fathima was 5k.
Now after 10 years the age of Rafi will be 7k + 10 and the age of Fathima will be 5K + 10.
Now it is given that the ratio of their age after 10 years is 9 : 7.
Now the ratio is nothing but a representation of a fraction. Hence we have
$\dfrac{7k+10}{5k+10}=\dfrac{9}{7}$
Cross multiplying the equation we get
$7\left( 7k+10 \right)=9\left( 5k+10 \right)$
Now let us open the bracket and multiply the terms
$49k+70=45k+90$
Taking 45k to LHS and 70 to RHS we get
49k – 45k = 90 – 70
4k = 20
Now dividing the equation by 4 we get k = 5.
Now present age of Rafi is 7k and present age of Fathima is 5k
Hence present age of Rafi is 7 × 5 = 35
and the present age of Fathima is 5 × 5 = 25.

Note: Note that when the ratio of age is given as 7 : 5. We cannot take the ages to be 7 and 5.
We will have to consider the constant k. For example consider the fractions $\dfrac{7}{5},\dfrac{14}{10},\dfrac{21}{15},\dfrac{28}{20},\dfrac{35}{25}$
All these fractions are equal and their simplest form if $\dfrac{7}{5}$ .