the ratio of a two digit number and the number obtained by interchanging the digits is 4 : 7 if the difference of the digits is 3 find the number
Answers
Given that:
- The ratio of a two digit number and the number obtained by interchanging the digits is 4 : 7.
To Find:
- The required number.
Let us assume:
- Ten's digit of a number be x.
- Ones digit by y.
Required number = 10x + y
Number after interchanging the digits = 10y + x
According to the question.
↠ (10x + y) : (10y + x) = 4 : 7
↠ (10x + y) / (10y + x) = 4 / 7
Cross multiplication.
↠ 7(10x + y) = 4(10y + x)
↠ 70x + 7y = 40y + 4x
↠ 70x - 4x = 40y - 7y
↠ 66x = 33y
↠ 66x/33 = y
↠ 2x = y
↠ y = 2x (i)
From eqⁿ (i) we can say that the value of y is greater than x.
The difference of the digits is 3.
↠ y - x = 3
↠ y = 3 + x (ii)
Comparing eqⁿ (i) and eqⁿ (ii):
↠ 2x = 3 + x
↠ 2x - x = 3
↠ x = 3
Putting the value of x in eqⁿ (i):
↠ y = 2x
↠ y = 2(3)
↠ y = 6
Finding the required number:
↣ Number = 10x + y
↣ Number = 10(3) + 6
↣ Number = 30 + 6
↣ Number = 36
Hence,
- The required number is 36.
Answer :-
Required number
• Given :-
- The ratio of a two digit number and the number obtained by interchanging the digits is 4 : 7
- Difference of the digits is 3
• To Find :-
- Number = ?
• Solution :-
- Let ten's digit of a number be m
- And one's digit of a number be n
- So, required number = 10m + n
- And number after interchanging digits = 10n + m
A/q,
➪
➪
➪
⌬ By cross multiplication :-
➪
➪
➪
➪
➪
➪
➪
Also,
- Difference of digits is 3
Therefore,
➪ n - m = 3
➪
⌬ From [eqⁿ (1)] and [eqⁿ (2)], we get :-
➪ 2m = 3 + m
➪ 2m - m = 3
⌬ Putting value of 'm' in [eqⁿ (1)] :-
➪ n = 2 × 3
Now,
➪ Required number = 10m + n
⌬ Putting all known values :-
➪ Required number = (10 × 3) + 6
➪ Required number = 30 + 6