1)Raj’s age after 15 year will be 5 times his age 5 years
back, What is the present age of Raj?
a)12 b)13 c)10 d)11
Sol: Let us assume the Raj’s present age be x year,
then
Raj’s age after 15 years=x+15
Raj’s age 5 years back=x-5
Relation
(x+15)=5*(x-5)
(x+15)=5x-25
15+25=5x-x
40=4x
x=10
Raj’s present age be 10 years,
Ans is c)10
2) Ages of Ram and Sham is differ by 16 years. If 6 year
ago, the Ram was 3 times as old as the sham. Find their present ages.
Sol: Let us assume the Sham’s present age be x year,
Ram’s
present age be x+16 year
6 year ago
Sham’s
age be x-6 years,
Ram’s
age be x+16-6 years
As per condition
(x+16-6)=3(x-6)
x+10=3x-18
10+18=3x-x
28=2x
x=14
Sham’s present age be 14 years,
Ram’s present age be 30 years
3)Present age of the father is 3 years more than three
times age of his son. Three years hence fathers age will be 10 years more than
twice the age of the son. Find the present age of the father.
Sol: Let us
assume the son’s present age be x years,
Fathers
present age be 3x+3
3 years hence
son’s
age be x+3 years,
Fathers
age be (3x+3)+3
As per condition
(3x+3)+3=2(x+3)+10
3x+6=(2x+6)+10
3x+6=2x+16
3x-2x=16-6
x=10
hence fathers present age be 3x+3=(3*10+3)=33 years
4)Sanjay was 4 time as old as his son 8 years ago. After
8 years, Sanjay will be twice as old as his son. What are their present ages?
Sol:
Let
us assume son’s age 8 years ago be x
Sanjay’s
age 8 years ago is 4x
Present age
Son’s
present age be x+8
Sanjay’s
present age is 4x+8
Condition 8 year after
Son’s
age 8 years after be (x+8+8)=(x+16)
Sanjay’s
age 8 years after is (4x+8+8)=(4x+16)
(4x+16)=2(x+16)
4x+16=2x+32
4x-2x=32-16
2x=16
x=8
Son’s age 8 years ago is 8 years
Son’s present age (8+8)=16 years
Sanjay’s present age is (4*8+8)=32+8=40 years
5)One year ago, the ratio of Sachin’s and Sameer’s age
was 6:7 respectively. Four years hence, this ratio would become 7:8. How old is
Sachin?
Sol:
Let
us assume Sachin’s and Sameer’s one year ago age ratio be 6x:7x
Present age ratio
Present
age of Sachin’s and Sameer’s is 6x+1:7x+1
Four years hence
Four years after Sachin’s and Sameer’s age ratio is
6x+1+4:7x+1+4
Condition
(6x+5)/(7x+5)=7/8
8(6x+5) = 7(7x+5)
48x+40 = 49x+35
40-35= 49x-48x
5=x
Hence the Sachin’s present age is (6x+1)=(6*5+1)=30+1=31
years.
6)Suresh is younger than Rohit by 4 years. If their ages
are in the respective ratio of 7:9. How old is Suresh?
Sol: Let us
consider Rohit’s age as x
Suresh’s
age is x-4
Condition
(x-4)/x
= 7/9
9(x-4)=7x
9x-36=7x
9x-7x=36
2x=36
x=18
hence Suresh’s age is (18-4)=14 years
7) Six years ago, the ratio of the ages of Kranti and
Sandesh was 6:5. Four year hence the ratio of their ages will be 11:10, What is
Sandesh’s present age?
Sol:
Let
ages of Kranti and Sandesh 6 years ago be 6x:5x respectively
Present age ratio is 6x+6:5x+6
After 4 years
Ratio
of ages of Kranti and Sandesh will be 6x+6+4:5x+6+4
Condition
(6x+10)/(5x+10)=11/10
10(6x+10)=11(5x+10)
60x+100=55x+110
60x-55x=110-100
5x=10
x=2
hence Sandesh’s present age is (5x+6)=16 years
8) Sachin is younger than Rahul by 4 years. If their ages
are in the respective ratio of 7:9. How old is Rahul?
Sol: Let us
assume Sachin’s age as x
Rahul’s
age will be x+4
Condition
x/(x+4)=7/9
9x=7(x+4)
9x=7x+28
9x-7x=28
2x=28
x=14
Hence Rahul’s age will be x+4=18 years
9) The ratio between the present age of A and B is 6:7.
If B is 4 years old than A, what will be the ratio of ages of A and B after 4
years?
Sol: Let
ratio of present ages of A and B is 6x:7x
B is
4 year old than A
7x=6x+4
7x-6x=4
x=4
Ratio
after 4 years
(6x+4):(7x+4)
(24+4):(28+4)
(28):(32)
7:8
So required ratio of ages is 7:8.
10) The ratio between the present ages of A and B is 5:7
respectively. If the difference between B’s present age and A’s age after 6
years is 2. What is the total of A’s and B’s present ages?
Sol: Ratio
of present ages A and B is 5x:7x
Condition
7x-(5x+6)=2
7x-5x-6=2
2x=2+6
2x=8
x=4
present ages of A is 5x=20 years
present ages of B is 7x=28 years
total of A’s and B’s present ages is 48 years
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