Question

5.
In a two digit number, digit at the ten's place is twice the digit at units's
place. If the number obtained by interchanging the digits is added to the
original number, the sum is 66. Find the number.​

Answer 1

$\rm{\bold{\huge{Answer\dots}}}$

Number = 42

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Let the -

• unit digit be M
• ten's digit be N

In a two digit number, ten's digit is twice the unit digit.

Number = 10N + M

$\implies\:N\:=\:2\:\times\:M$

$\implies\:N\:=\:2M$ ...(1)

Now, the number obtained by interchanging the number is added to the original number. Then, their sum is 66.

Interchanged number = 10M + N

$\implies\:10N\:+\:M\:+\:10M\:+\:N\:=\:66$

$\implies\:11N\:+\:11M\:=\:66$

$\implies\:11(N\:+\:M)\:=\:66$

$\implies\:N\:+\:M\:=\:6$

$\implies\:2M\:+\:M\:=\:6$ [From (1)]

$\implies\:3M\:=\:6$

$\implies\:M\:=\:2$

Substitute value of N in (1)

$\implies\:N\:=\:2(2)$

$\implies\:N\:=\:4$

$\therefore$ Number = $10(4)\:+\:2$

$\implies\:42$

•°• Original number is 42.

Answer 2

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• ten's place is twice the digit at units's
• after interchanging sum of both 60 ..

$\LARGE\underline{\underline{\sf \red{S}\blue{o}\green{l}\orange{u}\pink{t}\purple{i}\orange{o}\red{n}:}}$

Let the original number be = 10x+y

x = 2y -----------------------------Equation (1)

After interchanging the number will be (10y+x) .

Accoding To Question Now,

it is given that, when both add their sum is 66.

so,

10x + y + 10y + x = 66

11x + 11y = 66

11(x+y) = 66

(x+y) = 6 ---------------------------- Equation (2)

Putting value of x from Equation (1) in Equation (2)

we get,

(2y+y) = 6

3y = 6

y = 2

so, x = 2×2 = 4 ..

so, out original number is = 10x + y = 10×4 +2 = 42 (Ans)

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$\large\red{\sf\underline{\underline{\:Verification:\:\:}}}$

42 + 24 = 66 (Proved)