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

Step-by-step explanation:

completely explained

Answer 2

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

• 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,

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

$➪ \sf \dfrac{Two\: digit\: number}{Interchanged\:number} = \dfrac{4}{7}[/tex[</p><p> </p><p></p><p> </p><p> </p><p></p><p>[tex]➪ \sf \dfrac{10m + n}{10n + m} = \dfrac{4}{7}$

⌬ By cross multiplication :-

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

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

$➪ \sf 70m + 7n = 40n + 4m$

$➪ \sf 70m - 4m = 40n - 7n$

$➪ \sf 66m = 33n$

$➪ \sf \dfrac{66m}{33}$

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

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

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

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