When 1 is added to each of two numbers their ratio becomes 1:2and when 5 is subtracted from each of them ,their ratio is 5:11.The difference of the numbers is
Answers
Step-by-step explanation:
Given :-
When 1 is added to each of two numbers their ratio becomes 1:2and when 5 is subtracted from each of them ,their ratio is 5:11
To find :-
Find the difference of the numbers?
Solution :-
Let the required numbers be X and Y
If 1 is added to the numbers then they becomes
(X+1) and (Y+1)
Their ratio = (X+1):(Y+1)
Given that
When 1 is added to each of two numbers their ratio becomes 1:2
=> (X+1):(Y+1) = 1:2
=> (X+1)/ (Y+1) = 1/2
On applying cross multiplication then
=> 2(X+1) = 1(Y+1)
=> 2X+2 = Y+1
=> Y+1 = 2X+2
=> Y = 2X+2-1
=> Y = 2X+1 -------------(1)
If 5 is subtracted from each of them they becomes (X-5) and (Y-5)
Their ratio = (X-5):(Y-5)
Given that
when 5 is subtracted from each of them ,their ratio is 5:11.
=> (X-5):(Y-5) = 5:11
=> (X-5)/(Y-5) = 5/11
On applying cross multiplication then
=> 11(X-5) = 5(Y-5)
=> 11X-55 = 5Y-25
=> 11X-5Y = -25+55
=> 11X-5Y = 30 --------(2)
On Substituting the value of Y in (2) ,from (1)
=> 11X -5(2X+1) = 30
=> 11X -10X-5 = 30
=> X -5 = 30
=> X = 30+5
=> X = 35
On Substituting the value of X in (1)
=> Y = 2(35)+1
=> Y = 70+1
=> Y = 71
The value of X = 35
The value of Y = 71
The difference of the numbers
= 71-35
= 36
Answer:-
The difference of the given numbers is 36
Check :-
X = 35 and Y = 71
When 1 is added to each of two numbers their ratio becomes 1:2
=> (35+1):(71+1)
=> 36:72
=> 1:2
when 5 is subtracted from each of them ,their ratio is 5:11
=>(35-5):(71-5)
=> 30:66
=> 5:11
Verified the given relations in the given problem
Used Method :-
- Substitution method
Step-by-step explanation:
Let the no.s be x and y.
given, A/Q,
x+1:y+1=1:2
y+1
x+1
=
2
1
2x+2=y+1
2x−y=−1 (1)
Again, x−5:y−5=5:11
y−5
x−5
=
11
5
11x−55=5y−25
11x−5y=30 (2)
from 1 and 2, by elimination method,
(1)×5⇒10x−5y=−5
(2)×1⇒11x−5y=30
−1x=−35,so,x=35
We know, from (1)
2x−y=−1
putting x==35, we get
2×35+1=y
71=y
so the no are 30 and 71.
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