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Finding Ages…! [AGE#1]

Hello friends, here we are presenting some very basics “AGE” related problems on quantitative aptitude. Go through these questions as these are one of the types of questions which come in most of the competitive examinations as well as in CBSE PSA papers.

AGE#1.Ten years ago, Ravi was half of Priya’s age. If the ratio of their present ages is 3:4, what is the difference between their present ages?

a. 35

b. 20

c. 15

d. 5

Solution: To solve these types of questions you should have a very basic knowledge of ratios and forming equations. Try to split up the question into smaller segments so as to form simple equations. If you are a newbie then we would suggest you to go through the simple steps which are written underneath and try to understand the concept.

Let us suppose that present age of Ravi be x and that’s of Priya be y.

In the question its given that – “Ten years ago…”. Therefore we can write that ten years before Ravi’s age was (x-10) and that of Priya was (y-10). So according to the first line we can write that,

(10 yrs before) , Ravi’s age = ½ of Priya’s age

Or, (x-10) = ½ (y-10)

Or, 2 (x -10) = (y -10)   (* transposition)

Or, 2x -20 = y – 10

Or, 2x = y-10+20

Or, x = (y+10)/2     ———— (1)

Now, lets try to form an equation from the details given in the 2nd statement of the question i.e. “If the ratio of their present ages is 3:4”. According to the 2nd statement we can write

Ravi’s age : Priya’s age = 3:4

Or, x:y = 3:4

Or, x/y = ¾

Or, x = 3y/4         ———————– (2)

Comparing (1) and (2) we can write,

(y+10)/2 = 3y/4

Or, 4 ( y+ 10) = 2 (3y)

Or, 4y +40 =6y

Or, 6y – 4y = 40

Or, 2y =40

Or, y = 40/2

Or, y = 20 , so present age of Priya is 20 years and from this we can easily find Ravi’s age by simply putting the value of y in any of the equations which we got earlier. So, putting the value of y in (2) we get,

X= (3y)/4

Or, X= (3×20)/4

Or, X = 60/4

Or, x = 15 yrs. So,we got Ravi’s age as 15 yrs. Therefore the difference between their ages is (20-15)= 5 years. Correct option is (d).

ages

One Comment

  1. This question can also be solved by using one variable. Comment on it and let us know if you need other methods to solve this same question.

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