Question

In a two digit number the sum of the digits is 7. If the number with the order of its digits reversed is 28 greater than twice the unit's digit of the original number, Find the number

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Answer 1

ɢɪᴠᴇɴ :-

In a two digit number the sum of the digits is 7. If the number with the order of its digits reversed is 28 greater than twice the unit's digit of the original number

Tᴏ ғɪɴᴅ :-

• Original number
• Reversed number

sᴏʟᴜᴛɪᴏɴ :-

Let tens place digit be x and ones place digit be y

then,

➲ According to 1st condition :-

• Ones place digit + Tens place digit = 7

• x + y = 7

• x = 7 - y --(1)

➲ According to 2nd condition :-

• Original number = (10x + y)
• Reversed number = (10y + x)

• Reversed no = 28 + 2 × ( Ones place)

↣ (10y + x) = 28 + 2 × y

↣ 10y + x = 28 + 2y

↣ 10y - 2y + x = 28

↣ 8y + x = 28

↣ x = 28 - 8y --(2)

From (1) and (2) , we get,

↣ 7 - y = 28 - 8y

↣ 8y - y = 28 - 7

↣ 7y = 21

↣ y = 21/7

↣ y = 3

Put y = 3 in (1) , we get,

↣ x + y = 7

↣ x + 3 = 7

↣ x = 7 - 3

↣ x = 4

Hence,

• Tens place digit = x = 4
• Ones place digit = y = 3

Therefore,

• Original no (10x + y) = 43
• Reversed no (10y + x) = 34

Answer 2

$\large\bf\underline{Given:-}$

• Sum of digits = 7
• The reversed number is 28 greater than twice the unit's digit of the original number.

$\large\bf\underline {To \: find:-}$

• The number.

$\huge\bf\underline{Solution:-}$

• Let the ten's place digit be x
• Let the unit's place digit be y

So the number = 10x + y

★ Sum of digits (x + y ) = 7

⠀⠀⠀⠀⠀➝ x = 7 -y ......(i)

Reversed number = 10y + x

$\underbrace{ \bigstar \: \bf \:According \: to \: question }$

If the number with the order of its digits reversed is 28 greater than twice the unit's digit of the original number.

$\dashrightarrow\rm\:10y + x = 28 + 2y \\ \\ \dashrightarrow\rm\:10y - 2y + x = 28 \\ \\ \dashrightarrow\rm\:8y + x = 28..........(ii) \\ \\ \: \: \: \dag \rm \: substituting \: value \: of \: x \: from \: (i) \: in \: eq.(ii) \\ \\ \longrightarrow \rm \: 8y + (7 - y) = 28 \\ \\ \longrightarrow \rm \: 8y + 7 - y = 28 \\ \\ \longrightarrow \rm \: 7y + 7 = 28 \\ \\ \longrightarrow \rm \: 7(y + 1) = 28 \\ \\ \longrightarrow \rm \: y + 1 = \frac{28}{7} \\ \\ \longrightarrow \rm \: y + 1 = 4 \\ \\ \longrightarrow \rm \: y = 3 \\ \\ \rm \dag \: substituting \: value \: of \: y = 3\: in \: eq.(i) \\ \\ \: \longmapsto\rm \: x = 7 - y \\ \\ \: \longmapsto\rm \: x = 7 - 3 \\ \\ \: \longmapsto\rm \: x = 4$

Hence we get,

• ten's place digit (x) = 4
• unit's place digit (y) = 3

So the original number 10x + y

• 10 × 4 + 3
• 40 + 3
• 43

Reversed number 10y + x

• 10 × 3 + 4
• 30 + 4
• 34