**PROBLEMS ON AGES**

1. Present ages of Sameer and Anand are in the ratio of 5 : 4 respectively. Three years hence, the ratio of their ages will become 11 : 9 respectively. What is Anand’s present age in years?

**a. 24 ** b. 27 c. 40 d. None of these

**Basic Formula:**

If the present age of A is ‘x’ years, the age of A, n years ago was (x-n) years, and the age of a after n years will be (x+n) years.

**Answer with Explanation:**

Given : The ratio of the present ages of Sameer and Anand is 5:4

Let the present ages of Sameer be 5x years

Let the present ages of Anand be 4x years

Given: 3years hence (after), the ratio is 11 : 9

5x + 3 : 4x + 3

11 : 9

(5x+3) 9 = 11 (4x + 3)

45x +27 = 44x +33

45x -44x = 33-27

X = 6

To find: Present age of Anand

**The present age of Anand is 4(6) years = 24 years **

2. The ratio of the present ages of two brothers is 1 : 2 and 5 years back, the ratio was 1 : 3. What will be the ratio of their ages after 5 years?

a. 1 : 4 b. 2 : 3 **c. 3 : 5 ** d. 5 : 6

**Answer with Explanation:**

Let the two brothers be X and Y

Given: The ratio of the present ages of X and Y is 1:2

Let the present age of X be x years

Let the present age of Y be 2x years

** **X : Y

x : 2x

Given : 5 years back (before), the ratio was 1:3

x-5 = 1 : 2x-5 = 3

= 1/3

3 (x-5) = 2x-5

3x-15 = 2x-5 3x-2x = -5 +15 x = 10

To find : The ratio of their ages after 5 years

X+5 = ? : 2x + 5 = ?

10 + 5 = 15 : 2(10)+5 = 25

15 : 25 ** 3 : 5**

3. The present ages of three persons are in proportions 4 : 7 : 9. Eight years ago, the sum of their ages was 56. Find their present ages (in years).

a. 8, 20, 28 **b. 16, 28, 36** c. 20, 35, 45 d. None of these

**Answer with Explanation:**

Let the 3 persons be A, B and C

Given : The ratio of the present ages of 3 persons is 4:7:9

Let the present age of A be 4x years

Let the present age of B be 7x years

Let the present age of C be 9x years

A : B : C 4x : 7x : 9x

Given : 8 years ago, the sum of their ages was 56.

8 years ago, the ratio of the ages is

A : B : C 4x – 8 : 7x – 8 : 9x – 8

Given : The sum of the above ages was 56

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

20x – 24 = 56 20x = 56+24 20x=80

x = 4

To find : A, B and C’s present age.

A : B : C

4x : 7x : 9x 4 (4) : 7 (4) : 9 (4)

** A’s Age = 16 ; B’s Age = 28 ; C’s Age = 36**

4. The ratio between the present ages of A and B is 5 : 3 respectively. The ratio between A’s age 4 years ago and B’s age 4 years hence is 1 : 1. What is the ratio between A’s age 4 years hence and B’s age 4 years ago?

a. 1 : 3 b. 2 : 1 **c. 3 : 1 ** d. 4 :

**Answer with Explanation:**

Given : The ratio between the present ages of A and B is 5 : 3

Let the present age of A is 5x years

Let the present age of B is 3x years

Given : The ratio between A’s age 4 years ago and B’s age 4 years hence is 1:1

A’s age 4 years ago = 5x - 4

B’s age 4 years hence = 3x + 4

5x-4 = 1 ; 3x +4 = 1

= 1/1

5x-4 = 3x +4 5x – 3x = 4 + 4 2x =8 x = 4

**To find : **

5x+4 = ? : 3x - 4 = ?

20 + 4 = 24 : 12 – 4

24 : 8 **3 : 1**

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