**Q1. Difference between the ages of two persons is 20 years. If 5 years ago, the older one was five times as old as the younger one. Find their current ages.**

A. Let the current age be x and y.

So, x – y = 20 … eq.1

Four years ago…

(x – 5) = 5(y – 5)

x – 5 = 5y – 25

x – 5y = -20 … eq.2

On solving both equations, we get :

x = 30 and y = 10.

**Q2. Ratio of Geek’s and Chef’s is 12 : 15 respectively. After 10 years, the ratio of their ages will be 14 : 17. Find the difference in their ages.**

A. Let geek’s age be 12x and chef’s age be 15x.

After 10 years, their ratio becomes 14 : 17,

So,

204x + 170 = 210x + 140

30 = 6x

x = 5

So, difference in their ages = 15 * 5 – 12 * 5 = 15 years.

**Q3. The ratio of ages of a father and his son is 11 : 5 respectively. 6 years ago the ratio of their ages was 5 : 2 respectively. Find father’s present age ?**

A. Let the present age be 11x and 5x for father and his son respectively.

Also, 6 years ago, ratio of their ages was 5/2.

So,

22x – 12 = 25x – 30

3x = 18

x = 6

So, Father’s age = 11 * 6 = 66 years.

**Q4. Sita and Gita are best friends. Their product of ages is 120. If twice the age of Gita is more than Sita’s age by 8 years, what is Gita’s age ?**

A. Let Sita’s age be x. Then, Gita’s age be 120/x years.

So,

x = 12

So, Gita’s age = 120/12 = 10 years.

**Q5. Lovely’s age after six years will be three-seventh of his father’s age. Ten years ago, the ratio of their ages 1 : 5. What is Lovely’s father’s age now ?**

A. Let the ages of lovely and his father 10 years ago be x and 5x years respectively.

Lovely’s age after 6 years will be three-seventh of his father’s age.

7(x + 16) = 3(5x + 16)

8x = 64

x = 8.