**Important Formulas Shortcuts on “Problems on Ages” :**

**1.**If the current age is x, then n times the age is

**nx.**

**2.**If the current age is x, then age n years later

**= x + n.**

**3.**If the current age is x, then age n years ago

**= x – n.**

**4**. The ages in a ratio of a : b will be ax and

**bx.**

**5.**If the current age is x, then 1/n of the age is

**x/n.**

**6**. Difference age of two persons in present time is same as in n time after and before

**1.Father is aged three times more than his son Sunil. After 8 years, he would be two and a half times of Sunil’s age. After further 8 years, how many times would he be of Sunil’s age?**

**2. The sum of ages of 5 children born at the intervals of 3 years each is 50 years. What is the age of the youngest child?**

**3.A man’s age is 125% of what it was 10 years ago, but 83 1/3 % of what it will be after ten 10 years. What is his present age?**

**4. A father said to his son, “I was as old as you are at the present at the time of your birth”. If the father’s age is 38 years now, the son’s age five years back was:**

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

**6. Six years ago, the ratio of the ages of Kunal and Sagar was 6 : 5. Four years hence, the ratio of their ages will be 11 : 10. What is Sagar’s age at present?**

**7. The Average age of a class of 22 students is 21 years. The average increased by 1 when the teacher’s age also included. What is the age of the teacher?**

**8.My brother is 3 years elder to me. My father was 28 years of age when my sister was born while my mother was 26 years of age when I was born. If my sister was 4 years of age when my brother was born, then what was the age my father when my brother was born?**

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

**10.The ages of two persons differ by 16 years. 6 years ago, the elder one was 3 times as old as the younger one. What are their present ages of the elder person?**

**ANSWERS AND SOLUTION :**

**1(C)Explanation :**

Assume that Sunil’s present age = x.

Then father’s present age = 3x + x = 4x

After 8 years, fathers age = 2 ½ times of Sunils’ age

=> (4x+8) = 2 ½ × (x+8)

=> 4x + 8 = (5/2) ×(x + 8)

=> 8x + 16 = 5x+ 40

=> 3x = 40-16 = 24

=> x = 24/3 = 8

After further 8 years,

Sunil’s age = x + 8+ 8 = 8+8+8 = 24

Father’s age = 4x + 8 + 8 = 4 × 8 + 8 + 8 = 48

Father’s age/Sunil’s age = 48/24 = 2

**2(A)Explanation:**

Let the ages of children be x, (x + 3), (x + 6), (x + 9) and (x + 12) years.

Then, x + (x + 3) + (x + 6) + (x + 9) + (x + 12) = 50

=> 5x = 20

=> x = 4.

So Age of the youngest child = x = 4 years.

**3(C)Explanation :**

Let the age before 10 years = x

Then 125x/100 = x + 10

=>125x = 100x + 1000

=> x = 1000/25 = 40

Present age = x + 10 = 40 +10 = 50

**4(A)Explanation:**

Let the son’s present age be x years. Then, (38 – x) = x

=>2x = 38.

=> x = 19.

So Son’s age 5 years back (19 – 5) = 14 years.

**5(D)Explanation :**

Ratio of the present age of Kiran and Syam = 5 : 4

=> Let the present age of Kiran = 5x

Present age of Syam = 4x

After 3 years, ratio of their ages = 11:9

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

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

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

=> 45x + 27 = 44x + 33

=> x = 33-27 =6

Syam’s present age = 4x = 4×6 = 24

**6(A)Explanation:**

Let the ages of Kunal and Sagar 6 years ago be 6x and 5x years respectively.

Then, ((6x + 6) + 4)/(5x + 6) + 4 = 11/10

=> 10(6x + 10) = 11(5x + 10)

=> 5x = 10

=> x = 2.

So Sagar’s present age = (5x + 6) = 16 years.

**7(D)Explanation :**

Total age of all students = 22×21

Total age of all students + age of the teacher = 23 × 22

Age of the teacher = 23×22 – 22×21 = 22(23-21) = 22×2 = 44

**8(D)Explanation :**

Let my age = x

Then

My brother’s age = x + 3

My mother’s age = x + 26

My sister’s age = (x + 3) + 4 = x + 7

My Father’s age = (x + 7) + 28 = x + 35

=> age my father when my brother was born = x + 35 – (x + 3) = 32

**9(B)Explanation:**

Let their present ages be 4x, 7x and 9x years respectively.

Then, (4x – 8) + (7x – 8) + (9x – 8) = 56

=> 20x = 80

=> x = 4.

So Their present ages are 4x = 16 years, 7x = 28 years and 9x = 36 years respectively.

**10(C)Explanation :**

Let’s take the present age of the elder person = x

and the present age of the younger person = x – 16

(x – 6) = 3 (x-16-6)

=> x – 6 = 3x – 66

=> 2x = 60

=> x = 60/2 = 30

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Refresh!!!

SSC CGL 2015: English Quiz

http://www.sscadda.com/2015/05/ssc-cgl-2015-english-quiz_19.html

mam please give questions on ratio and proportion and time and distance too.