Question

At present, the ratio between the age of Sharmila and Sanju is \[5:7\] respectively. If Sharmila is 12 years younger than Sanju, what is the total of ages of Sharmila and Sanju 4 years ago?

Answer 1

Hint: Here the ratio between the age of two persons is given, also the difference between their age is given. So the difference in the ratio can be equated to the difference between the age. So that we will get their actual age and then reducing it by 4 we will get the required sum.

Complete step by step answer:

Given that,
The ratio of their ages is \[5:7\].
Let the age ratio be \[5x:7x\].
It is also given that Sharmila is 12 years younger than Sanju.
So the difference in their age is 12 years.
Now the difference in their age is equal to the difference in the ratio also.
Thus,
 \[
  7x - 5x = 12 \\
   \Rightarrow 2x = 12 \\
   \Rightarrow x = 6 \\
\]
So putting this value in ratio of their ages we will get their present age.
Sharmila’s age \[5x = 5 \times 6 = 30years\]
Sanju’s age \[7x = 7 \times 6 = 42years\]
This is their present age, but we are asked to find the total of ages of Sharmila and Sanju 4 years ago.
So first reduce 4 years from their age and then add or reduce 8 years from the total of their present age.
So, \[(30 + 42) - 8 = 64years\]
Or
\[(30 - 4) + (42 - 4) = 64years\]
So the correct answer is 64 years.

Note: Remember we are given with ratio of their present ages. And also note that age either increases or decreases the ratio will not change.so if you observe that even after reducing four years from their ages ration is\[5:7\].