Problems in calculating the age of an individual are very common in the quantitative aptitude section. In the present article, we will discuss the Ratio Based Age Problems. In such problems, the ages of two or more people will either be such that they bear a ratio or they will have some relation by which we can get a ratio. Here we will see how to solve these problems. We will also develop formulae and shortcuts that will save us a lot of precious time. Let us start by defining what we mean by a ratio.
Ratio-Based Age Problems
We may define the ratio of two quantities as the quantitative relation between their two amounts that tells us the number of times one of these quantities contains the other. We can get the ratio of any two quantities by dividing them with each other until we get prime numbers on both the numerator and the denominator or at least on one of them. For example, if ‘m’ is any quantity and ‘n’ is another quantity then the ratio of m and n, which we pronounce as m” is to” n is = m/n and we write it as m:n. This ratio gives the comparison in terms of the magnitude of the two quantities.
Let us now focus on the problems of age, in particular, the ratio-based word problems. Let us start with a simple example.
Example 1: A brother and a sister decide to find the ratio of their ages. The ratio comes out to be 4:5 respectively. Which of the two is the elder one?
Answer: This is a straightforward question to make you better understand the concept of ratios. Let x denote the age of the brother and y denote the age of the sister. The as per the question, the ratio is x/y = 4/5. upon cross-multiplication, we have: 5x = 4y or in other words y > x. Thus the sister is the elder one.
Solved Examples On Age
Example 2: The ratio of the age of a person A and another person B is 1:3. If the person A is 5 years younger than the person B, then what are their ages?
A) 2 and 7 years respectively
B) 7 and 2 years respectively
C) Two and a half and seven and a half years respectively
D) Seven and a half and two years respectively
Answer: Let A denote the age of the person A and B denote the age of the person B. As per the questions, the age of person A/B = 1/3.
Also as per the second condition, we have A = B – 5, using this in the above ratio, we have:
(B – 5)/B = 1/3 or 3B – 15 = B
Hence we have 2B = 15 or B = 7.5. Therefore the age of the second person B is 7 and a half years. Thus from the second condition i.e. A = B – 5 or A = 7.5 – 5 = 2.5, we can say that the age of the first person or A is two and a half years. Therefore the correct option is C) Two and a half and seven and a half years respectively
In this question you have to realize that only the ratio is not sufficient to predict the exact ages of the two people, rather we need to know some other condition too. Let us see another example.
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Example 2: Some six years ago, the ratio of the ages of Khan and Suhail was 6:5. Four years from today, the ratio of their ages will be 11:10. Then Suhail must be _______ years old.
A) 18 years B) 12 years C) 19 years D) 16 years
Answer: For simplicity, we shall assume that six years ago the age of Khan was 6x and the age of Suhail was 5x, where ‘x’ is an unknown variable. Let us see the first condition of the question. The ratio of their ages was 6:5 or 6x:5x respectively. For the second condition of the question, we will have to find the present age first.
The present age of Khan is 6x + 6 and that of Suhail is 5x + 6 respectively. Four years into the future, their ages will be 6x + 10 and 5x + 10 years respectively. Hence as per the second condition, we have:
(6x + 10)/(5x + 10) = 11/10 or 60x + 100 = 55x + 110.
We can write this as 5x = 10 or x = 2. Therefore the age of Suhail at the present must be = 5(2) + 6 = 16 years. Hence the correct option here is D) 16 years.
Q 1: Khan and Shoaib decide to take a ratio of their ages. It comes out to be 5:4 respectively. Three years from now, the ratio of their ages will be 11 : 9 respectively. What is Shoaib’s present age in years?
A) 37 years B) 27 years C) 46 years D) Cannot be determined E) None of these
Ans: A) 37 years
Q 2: Today the ratio of the ages of Desai and Shinde is 4:3. Six years hence, Desai’s age will be 26 years. How old is Shinde today?
A) 10 years B) 15 years C) 20 years D) 25 years
Ans: B) 15 years