## Ques 1.

One year ago, ratio of Siva and Ganesh age’s was 5 : 6 respectively. After 4 years, this ratio becomes 6 : 7. How old is Ganesh ?

**Solution :**

1 year ago Ratio = 5:6 ( Difference between ratio 6-5=1) ---(i)

4 years ago Ratio = 6:7 ( Difference between ratio 7-6=1)---(ii)

Difference = 1+4 = 5 years

New ratios :

1 year ago Ratio = 5:6 *1 (1 from equation ii) = 5:6

4 years ago Ratio = 6:7 *1 ( 1 from equation i) = 6:7

Ganesh age ratio difference = 7-6= 1 Unit

1 Unit ------ 5 years

6 Unit ------ ??

==> 1 year ago Ganesh ago = (6*5)/1 = 30 years

Present age of Ganesh = 30+1 = 31 years

## Ques 2.

Ten years ago, A was half of B in age. If the ratio of their present ages is 3:5, what will be the total of their present ages ?

**Solution :**

10 years ago Ratio = 1:2 ( Difference 2-1=1)

Present Ratio = 3:5 ( Difference 5-3=2)

New Ratios :

10 years ago ratio = 1:2 *2 = 2:4

Present ratio = 3:5 *1 = 3:5

Common Difference between ratio = 5-4 =1

= 3-2=1

1 unit --------- 10 years

8 Units ------- x

==> x = 80years

## Ques 3.

The age of Ravi 10 years ago was thrice the age of his son. Ten years hence, Ravi's age will be twice that of his son. The ratio of their present ages is ?

**Solution :**

10 years ago ratio = 3:1 ( Difference 2)

10 years hence ratio = 2:1( Difference 1)

New Ratios :

10 years ago ratio = 3:1 *1 = 3:1

10 years hence ratio = 2:1 *2 = 4:2

Total difference in years = 10+10 = 20 years

Common difference between ratio = 4-3= 1 Unit

1 Unit ----------- 20 years

4 Units -------- 80 years ( father)

2 units ------- 40 years ( son)

Present ages ratio = 80-10 : 40-10 = 70:30 = 7:3

## Ques 4.

The average age of a coaching institute of 15 students is 23. When the age of teacher is also included, the average will be increased by 3 years. What was the age of teacher two years ago?

**Solution :**

==> (23 +3) + (15*3 ) = 26+45 =71 years

2 years ago teacher ago = 71 - 2 = 69 years

## Ques 5.

A is younger than B by 8 years. If the ratio of their ages is 7:9, find the age of A ?

**Solution :**

Difference between ratio = 9-7=2

Age difference = 8 years

2 units ----------- 8

7 units ----------- x

==> x = 8*7/2 = 28 years

## Ques 6.

10 years before , the ratio of ages P and Q was 13: 17. After 17 years from now , the ratio of their ages will be 10:11 the present age of Q ?

**Solution :**

10 years ago Ratio = 13:17 ( Difference 17-13=4)

17 years ago Ratio = 10:11 ( Difference 11-10=1)

New Ratios :

10 years ago = 13:17 *1 = 13:17

17 years hence = 10:11 *4 = 40 : 44

Q ratio difference = 44-17=27

Total age difference = 10+17=27 years

27 units ---------- 27 years

17 units --------- ?

Q age 10 years ago = 17 years

Q present age = 17+10=27 years

## Ques 7.

The age of a man after 15 years is 4 times of the age of that man 15 years before . His present age is ?

**Solution :**

Present age = x

According to question

X+15 =4(x-15)

==> x =25 years

## Ques 8.

The average age of 8 children of a family is 12 years . If the age of 7 children are 12,8,14,11,9,13 and 15 years . Then the age of 8th child will be ?

**Solution :**

Total age of 8 children = 8*12=96

Total age of 7 children = 82

8th child age = 96-82=14 years

## Ques 9.

The ratio between A and B present ages is 3:8 . After 8 years , A's age will be 20 years . What was B's age 5 ago ?

**Solution :**

Present age of A = 20-8= 12 years

3 units ------- 12 years

8 units ------ x

==> B present age = x = 32 years

B age 5 years ago = 32-5=27 years .

## Ques 10.

The present age of A and B are 36 and 50 years . If after "n" years the ratio of their ages will be 3:4 , then find n value ?

Solution :

==> (36+n)/(50+n) = 3/4

==> n = 6 years