In a two - digit number, the unit's digit is 5 - less than the tens digit. The
number form by interchanging the digits and the original number are in the ratio
3:8. Find the number
please answer this question with a proper solution.
Answers
Step-by-step explanation:
Given:-
A two - digit number, the unit's digit is 5 - less than the tens digit. Thenumber form by interchanging the digits and the original number are in the ratio 3:8.
To find:-
Find the number ?
Solution:-
Let the digit at tens place be X
The place value of X = 10X
Then, The digit at ones place
= 5 less than the tens digit.
=X-5
Then the number
= 10X+X-5
=11X-5
The two digit number = 11X-5
If the digits are interchanged then the number
=10(X-5)+X
=10X-50+X
=11X-50
The ratio of the number form by interchanging the digits and the original number = 3:8
=> (11X-50):(11X-5) =3:8
=> (11X-50)/(11X-5) =3/8
On applying cross multiplication then
=> 8(11X-50)=3(11X-5)
=>88X-400 = 33X-15
=>88X-33X=-15+400
=>55X=385
=>X = 385/55
=>X=(11×35)/(5×11)
=>X = 35/5
=>X=7
The digit at 10s place = 7
The digit at ones place = 7-5 = 2
The two digit number = 72
Answer:-
The required two digit number for the given problem is 72
Check:-
Digit at 10's place = 7
Digit at 1's place = 7-5 = 2
The number = 72
The number formed by interchanging the digits
=27
Their ratio = 27:72
=>27/72
=>(3×9)/(8×9)
=>3/8
=>3:8
Verified the given relations