## Most Important Problems Based on Ages

Problem on ages is one of the easiest topic of Quantitative Aptitude section. Today, we will discuss about the basic approach and some previous year questions of Age based problems.
In this topic, you need to know basics of linear equations and ratio. You may across many formulas in this topic, but if you understand the basics well, you won’t need them. So, make sure that you clear your basics of the above two topics and practice well.

The main difficulty in this chapter is that students are not able to express given data in a proper manner, so solving these problems becomes a bit difficult.

Note -

- Try to make only one base variable and express other variables in terms of it.
- Read questions carefully and convert the given information in linear equation.

**We will discuss various questions asked in previous year exams.**

**Example 1. The ratio of A’s age 3 years ago and B’s age 5 years ago is 4:5. If A is 4 years younger than B then what is the present age of B? (IBPS CLERK PRE 2016)**

**Solution:**

**APPROACH 1:**Let assume at present A’s age is X and B’s age is Y.

Given, (X-3):(Y-5) = 4:5 and X = Y-4

Solve both equations and then get X and Y.

Now, we have to equations and two variables. Generally, this type of approach consumes more time and is not preferable.

**APPROACH 2:**In this type of question, assume only one variable i.e. called base variable. Let A’s present age is X, then B’s present age is X+4. Students often commit silly mistakes, they tick the option which have X value but present age of B is asked in question.

So,(A’s 3yrs ago):(B’s 5yrs ago) = 4:5(X-3): (X+4-5) = 4:5(X-3): (X-1) = 4:55X-15 = 4X-4X= 11 i.e. A’s Present ageand B’s present age is X+4 = 11+4 =15yrs.

**Example 2. A is 3 years older than B while B is 2 years younger than C. The ratio of age of A 4 years hence and B years ago is 5:3. What was the age of C 6 years ago?**

*(IBPS PO 2016 Pre)***Solution:**There are three variables in this question and students are often confused about which variables should be assumed as base variable. You can see in question relation of B with both A and C is mentioned. So, you can assume B as base variable. If you assume another one as base variable, there is a chance that calculation may become a little harder.

Let present age of B’s is X, then A’s age = X+3 and C’s age = X-2(Age of A 4yrs hence): (Age of B 4yrs ago) = 5:3(X+3+4): (X-3) = 5:3(X+7): (X-3) = 5:33X+21 = 5X-152X = 36X = 18

Present age of C is X-2 = 18-2 = 16yrs

Age of C 6yrs ago = 16-6 = 10yrs

Shortcut: (X+7): (X-3) = 5:3

difference of 5 and 3 is directly proportional to difference of (X+7)and(X-3)

So,(5-3) ∝ (X+7)-(X-3)

2 ∝ 10

1 ∝ 5

We can write X+7 = 5×5 , X = 18

Hence, age of C 6yrs ago = 10yrs

**Example 3. The average age of Atul, Jatin and Sonu is 24years. 2 year ago, average age of Atul and Sonu was 23yrs. 2yrs hence average age of Jatin and Sonu is 26 years. Find the present age of Sonu?**

*(IBPS PO 2016 Mains)***Solution:**Given, average age of Atul, Jatin and Sonu = 24 yrs

∴ total age of Atul, Jatin and Sonu = 24×3 = 72 yrs ….(1)

2yrs ago, average age of Atul and Sonu = 23

2yrs ago, total age of atul and sonu = 46

∴ present total age of atul and sonu = 50 ….(2)

2yrs hence, average age of Jatin and Sonu = 26

2yrs hence, total age of Jatin and Sonu = 52

∴ present total age of Jatin and Sonu = 48 …….(3)

From equation 1, 2 and 3

Present age of Sonu is 26 years.

**Example 4. The average age of A and B is 25 years. If C were to replace A, the average would be 24 and if C were to replace B, the average would be 26. What are the ages of A, B and C respectively?***(IPPB PO 2016 Pre)*

**Solution:**Given, avg. of (A+B) = 25

∴ (A+B) = 50

Avg. of (C+B) = 24

∴ (C+B) = 48

Avg. of (A+C) = 26

∴ (A+C) = 52

Now , A+B+C = (50+48+52)/2

A+B+C = 75

C = 25, A = 27, B = 23

**Example 5. The ages of Sona and Mona are in the ratio of 15:17 respectively. After 6 years, the ratio of their ages will be 9:10. What will be the age of Mona after 6 years?***(SBI Clerk 2016 Mains)*

**Solution:**Let present age of Sona is 15X, then Mona = 17X

Given, (15X+6) : (17X+6) = 9 : 10

150X+60 = 153X+54

3X = 6

X = 2 yrs

Age of Mona after 6yrs is (17×2+6) = 40yrs.

**Now, we will discuss questions which are asked by some of students.**

**Doubt Question 1. The present ages of A,B and C in proportion 4:7:9, eight years ago, the sum of their ages was 56. find their respective ages (in years)**

**Solution:**Let ratio of present ages of A,B and C is 4x:7x:9x

sum of their ages eight years ago = 56

(4x-8)+(7x-8)+(9x-8) = 56

20x = 80

x = 4

A = 4x = 16 years

B = 7x = 28 years

C = 9x = 36 years

**Doubt Question 2.**

**The sum of the ages of Rinku and Gopal is 40 years. 5 years hence ratio of their ages will be 3:7. Find the age of Rinku?**

**Solution:**Given 5yrs hence ratio of ages of Rinku and Gopal is 3:7

let 5yrs hence, age of Rinku = 3X and Gopal = 7X

So, present age of Rinku = 3X-5 and Gopal = 7x-5

Sum of present ages of Rinku and Gopal = 40

(3X-5)+(7X-5) = 40

10X = 50

X = 5

present age of Rinku = 3X-5 = 10yrs

**Doubt Question 3**.

**The present age of Romila is one-fourth that of her father. After 6 years the father’s age will be twice the age of Kapil. If Kapil celebrated fifth birthday 8 years ago. What is Romila’s present age?**

**Solution:**Let present age of Romila is X, then Father’s age = 4X

6 years hence,

father’s age = 4X+6

2 (Age of Kapil) = 4X+6

Age of Kapil = 2X+3

Present age of Kapil = 2X+3-6 = 2X-3

Kapil celebrated his 5th bairthday 8 years ago

So, Present age of Kapil is 5+8 = 13 years

2X-3 = 13

2X = 16

X = 8years.

Shortcut approach:Kapil celebrated his 5th birthday 8 years ago.Present age of Kapil = 13After 6years, father’s age will be twice of the Kapil.2x(13+6) = 4X+6X= 8 years

**Doubt Question 4. A man’s age is 133(1/3)% of what it was 8 years ago, but 80% of what it will be after 8 years. What is his present age?**

**Solution:**Let the present age be X years.

Then 133(1/3)% of (X-8) = X and 80%(X+8) = X

So, 133(1/3)% of (X-8) = 80%(X+8)

4(X-8)/3 = 4(X+8)/5

5(X-8) = 3(X+8)

2X = 64

X = 32

Shortcut approach:You don’t need to solve both equation. Solve any equation you will get the answer.133(1/3)% of (X-8) = X4(X-8)/3 = X4X-32 = 3XX = 32 years.

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