Important word problems on Linear Equations in two variables 9
Question for practice
Questions:9. The ratio of the ages of the father and the son at present is 3 : 1.
The following questions are more helpful for class tenth students for all boards.
Four year earlier, the ratio will become 4 : 1. What is the present
age of father and son?
Submit your answer here in the comments or wait for answer
let their ages be in the Ratio of 3x : 1x
ReplyDeletelet their ages 4 earlier be in the ratio of 4y : 1y
therefore :-
3x-4 = 4y - (A)
x-4 = y - (B)
x = y-4 - (C)
putting (C) in (A)
3y - 12 -4 = 4y
8 = y - (D)
putting (D) in (B)
x-4 = 8
x = 12
3x = 12.3
=36
the present age of son is 12 yrs
the present age of father is 36 yrs
let the age of father be x n that of son be y .
ReplyDeletex/y = 3/1
so, 3y = x
3y - x = 0 (1)
x-4/y-4 = 4/1
so, 4y - x = 12 (2)
from (1) and (2)
y = 12 (elimination)
therefore fathers age is 36 years (3y) and sons age is 12 years (y)
Ans.
ReplyDeleteLet father's present age = x years
Let son's present age = y years
x/y = 3/1
or x-3y = 0 ......(1)
(x-4)/(y-4) = 4/1
or x-4 = 4y-16
or x-4y = -12 ......(2)
By elimination from (1) and (2),
y = 12
x = 36
therefore, present age of father = 36 years
present age of son = 12 years
Let present age of father= x yrs. Sons age=y yrs
ReplyDeletepresent ratios: 3/1=x/y
x= 3y
x-3y=0
4 yrs earlier
fathers age: x-4
sons age: y-4
Ratios : 4/1 =x-4/y-4
4(y-4)= x-4
4y -16=x-4
4y-x=12
Frm 1 nd 2 we get
sons age = 12 yrs
fathers age= 36 yrs
Let present age of father= x yrs. Sons age=y yrs
ReplyDeletepresent ratios: 3/1=x/y
x= 3y
x-3y=0
4 yrs earlier
fathers age: x-4
sons age: y-4
Ratios : 4/1 =x-4/y-4
4(y-4)= x-4
4y -16=x-4
4y-x=12
Frm 1 nd 2 we get
sons age = 12 yrs
fathers age= 36 yrs
Let present age of father be x years
ReplyDeleteLet present age of son be y years
ratios: 3/1=x/y
x= 3y
x-3y=0
4 yrs earlier
fathers age: x-4
sons age: y-4
Ratios 4/1 =x-4/y-4
4(y-4)= x-4
4y -16=x-4
4y-x=12
By Elimination method
sons age 12 yrs
fathers age= 36 yrs
let their ages be in the Ratio of 3x : 1x
ReplyDeletelet their ages 4 earlier be in the ratio of 4y : 1y
.'.
3x-4 = 4y ~1
x-4 = y ~2
x = y-4 ~3
putting (3)in(1)
3y - 12 -4 = 4y
8 = y ~ 4
putting (4)in(2)
x-4 = 8
x = 12
3x = 12.3
=36
the present age of son is 12 yrs
the present age of father is 36 yrs
Let the present of father be x
ReplyDeleteLet the present of his son be y
The ratio of their present ages is 6:1
x/y=6/1
x=6y
x-6y=0 1
the ratio of their ages after 5 years will be 7:2
x+5/y+5=7/2
2(x+5)=7(y+5)
2x+10=7y+35
2x-7y=35-10
2x-7y=25 2
eqn1*2 -eqn2
2x-21y=0
2x-7y=25
- + -
-5y=-25
y=5
Substituting y=5 in eqn 1
x-6(5)=0
x-30=0
x=30
the present age of father is 30 years
the present age of his son is 5 years
let the present ages of father and son be x and y respectively
ReplyDeleteatq... x/y=3/1 x-4/y-4=4/1
3y=x x-4y=-12 (2)
3y-x=0 (1)
eliminating (1) and (2)
y=12 putting value of y in (1)
3*12-x=0
36-x=0
-x=-36
x=36
therefore, present ages of
father and son are 36yrs and 12 yrs respectively..
Let present age of father = x yrs.
ReplyDeleteSons age =y yrs
present ratios: 3/1=x/y
x= 3y
x-3y=0
then ...
4 yrs earlier
fathers age: x-4
sons age: y-4
Ratios : 4/1 =x-4/y-4
4(y-4)= x-4
4y -16=x-4
4y-x=12
Frm 1 nd 2 we get
sons age is = 12 yrs
fathers age is = 36 yrs
let age of father be x and age of son be y.
ReplyDeletex/y=3/1
3y=x
3y-x=0(1)
before 4 yrs
age of father=x-4
age of son=y-4
x-4/y-4=4/1
4y-x=12(2)
from (1) and (2)
age of son=12 yrs
age of father=36 yrs
Let father's age = x years
ReplyDelete" son's age = y years
So, 3y = x (obviously, x has to be bigger than y)
=> x - 3y = 0........(1)
Also, 4(y-4) = 1(x-4)
=> 4y - 16 = x - 4
=> x - 4y = -12.........(2)
Eliminating (1) and (2) we get
y = 12 and x = 36!!!
THANKS!!!