Question

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​

Answer 1

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 2

Answer :-

$\quad\pink{\bigstar}$ Required number $\leadsto\:{\boxed{\tt{\blue{36}}}}$

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• 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,

➪ $\sf Two \:digit\: number\: : \:Interchanged \:number = 4\: : \:7$

➪ $\sf \dfrac{Two\: digit\: number}{Interchanged\:number} = \dfrac{4}{7}$

➪ $\sf \dfrac{10m + n}{10n + m} = \dfrac{4}{7}$

⌬ By cross multiplication :-

➪ $\sf 7(10m + n) = 4(10n + m)$

➪ $\sf (7)(10m) + (7)(n) = (4)(10n) + (4)(m)$

➪ $\sf 70m + 7n = 40n + 4m$

➪ $\sf 70m - 4m = 40n - 7n$

➪ $\sf 66m = 33n$

➪ $\sf \dfrac{66m}{33} = n$

➪ $\sf \dfrac{\cancel{66}m}{\cancel{33}} = n$

$\bigstar\:\underline{\underline{\bf{\red{n = 2m}}}}\:\dashrightarrow\:{\bf{\green{[eq^{n}\:(1)]}}}$

Also,

• Difference of digits is 3

Therefore,

➪ n - m = 3

➪ $\bigstar\:\underline{\underline{\bf{\red{n = 3 + m}}}}\:\dashrightarrow\:{\bf{\green{[eq^{n}\:(2)]}}}$

⌬ From [eqⁿ (1)] and [eqⁿ (2)], we get :-

➪ 2m = 3 + m

➪ 2m - m = 3

$\bigstar\:\underline{\underline{\bf{\red{m = 3}}}}$

⌬ Putting value of 'm' in [eqⁿ (1)] :-

➪ n = 2 × 3

$\bigstar\:\underline{\underline{\bf{\red{n = 6}}}}$

Now,

➪ Required number = 10m + n

⌬ Putting all known values :-

➪ Required number = (10 × 3) + 6

➪ Required number = 30 + 6

$\bigstar\:\underline{\underline{\bf{\red{Required \:number = 36}}}}$

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